Can I save whats on my iMac harddrive if it doesnt boot

Yes, you can have the drive removed to try to recover what is on it. But if the drive has failed and is the cause of the boot failure, then the chances of recovering anything are slim. It really depends on why... what has caused the failure? Data corruption? Mechanical failure? You likely won't know until the drive is removed and you try to access it.

Check with your Apple Authorized Service Provider for that service.

First see if you can boot into Safe Mode by booting with the Shift key held down,

NOTE:  if you have a wireless keyboard with rechargeable batteries you should connect it with its charging cable to assure a boot into Safe Mode. 

If you can then try to reboot normally.

If you can't Boot into the Recovery volume (boot with the Command + R keys held down) and select the option to reinstall the system. Your data files will not be affected.

Are you telling us you have not been using Time Machine to backup your computer? If so, then you are about to learn a painful lesson on why backup is not a luxury but a necessity when operating ANY computer.

Please refer to Back up your Mac with Time Machine

The screenshot you provided shows "I/O Errors" for your boot disk so the hard drive is failing. You can try putting the iMac into Target Disk Mode to attempt to access the data. However, you need to be very careful since you can make the drive failure worse with each attempt to transfer files. macOS and third party data recovery apps are not made to handle a failing hard drive. If the drive failure is minor you can try using Carbon Copy Cloner (CCC) to transfer just the important data files first since CCC does have an option to ignore errors after a few have been encountered, but if the transfer is extremely slow, then it is best to abort copying the files or you risk making the drive failure so bad that even a professional data recovery service will be unable to retrieve any data.

You may want to consider contacting a professional data recovery service such as Drive Savers or Ontrack. Both vendors provide free estimates and both are recommended by Apple.

You usually only get one chance at recovering data from a failing hard drive so choose wisely.

You should always have frequent & regular backups. This is even more important on computers using an SSD since it is very difficult to impossible to recover data from an Apple SSD especially on the newer 2016+ USB-C Macs.

Once a hard drive begins to produce errors I would not want to continue using it. The errors usually just keep getting worse putting your data at risk.

It is not easy to repair an iMac. An iMac contains some very delicate easily damaged connectors which are hard to see and reach. Plus it is very easy to have the LCD Panel of a 27" model crack if not handled properly since the panel is so large and heavy.

Some iMac models require a special temperature sensor adapter when using a third party drive. You can check OWC's website to see if any temperature sensor adapter is needed plus OWC provides videos for replacing/upgrading the drives in an iMac. Keep in mind that those videos make it look much easier than it really is. If you decide to replace the failing hard drive I suggest upgrading to an SSD. Since a 2009 iMac only has a SATA II controller for the drives the most compatible SSD is the OWC Mercury Electra 3G SSD. Other SSDs may not be able to properly auto-negotiate the SATA Link Speed.

https://eshop.macsales.com/shop/ssd/owc/imac

Only you can decide whether it is cost effective to replace the hard drive since it does depend a lot on how you are using the iMac and whether it is still able to perform well for your needs. Keep in mind macOS on this iMac is now no longer supported by Apple so you are no longer receiving security updates. It will only be a matter of time before third party browsers will no longer be supported on this iMac. It is after all an eleven year old computer.

An Apple Store will not help you now since this iMac is considered "Obsolete". You would have to check your local Apple Authorized Service Provider to see whether they would be willing to upgrade the iMac to an SSD and how much it would cost. You can see if a regular computer shop/tech will perform the upgrade, but they may not be familiar with the Apple quirks of the iMac. Keep in mind labor may be $100 US.

It depends on the severity of the hard drive failure and whether the data you are trying to recover is located on a bad section of the drive. The safest and most reliable methods to recover the data is either by performing a low level bit for bit clone of the drive to an equal or larger drive using a command line utility (preferably from a Linux boot disk or Linux system) or by using a professional data recovery service such as Drive Savers or Ontrack as I mentioned in my earlier post.

If the data is not located on a bad section of the drive, then Carbon Copy Cloner may be able to transfer the files since it can be set to ignore the errors to some extent. Plus CCC does log the files copied (or at least the ones that are skipped). It is highly unlikely you will be able to use the Finder or a data recovery app to transfer the files since they are not designed to handle errors produced by a failing drive.

I have successfully recovered data from hundreds of failing Apple hard drives using the low level bit for bit clone using the command line utility GNU ddrescue which is designed for this purpose to concentrate on first recovering data from the good sections of the drive and ignoring the bad sections. After the good sections of the drive are recovered the utility can focus on the bad sections of the drive. However, many times by the end of the process the hard drive be dead. In fact is up to the user to determine when to stop the cloning process. Since it is a command line utility it is very easy to make a mistake such as mixing up the source & destination drives or attempting to access the cloned drive midway through the cloning process plus you destroy everything if your resume the clone without first reconfirming the source & destination drive identities.

While it is technically possible to use GNU ddrescue from a macOS boot drive I have found that macOS tends to interfere too much with the process many times making the drive failure even worse. Even if you get a good low level bit for bit clone, the clone may still need to have the file system repaired in order to access the data or a data recovery app may need to be used if the file system cannot be repaired. Even at this stage you may make a catastrophic mistake so I always like to either clone the cloned drive so I have a backup or I perform the initial clone to a raw image file which I then use to transfer the image to a good hard drive so if a mistake is made repairing the file system I can easily start over with a fresh copy of the image.

As you can see it can be very difficult and time consuming to attempt data recovery yourself although it is possible when you know what you are doing and are willing to risk permanently losing your data.

You may only get one chance to recover the data from a failing hard drive so make sure you choose wisely on how you attempt to recover the data. Basically if you attempt data recovery yourself and fail, then you may as well forget ever contacting a professional data recovery service since by that time you have probably made it impossible for them to recover the data.

A failing drive never gets better so it is a waste of time reinstalling macOS to a failing drive. It is your computer though so you can reinstall macOS if you want and perhaps it will work for a short time, but the failure will return. You do risk the integrity of any data you store on the failing drive.

Edit: You can try installing macOS to an external USB or Firewire drive, but you will find that the speed of the system will be very slow booting from USB. Plus the failing internal hard drive may affect the performance of the iMac even when booting from a good external drive depending on the severity of the failure of the internal drive.