MacBook Air Flickering Apple Logo and Cancel Symbol

The person you bought the computer from should have provided you with the disks that came with the computer. If they didn't, ask them for the disks. You can then boot off the disks and re-install the OS.

If your Air is a MacBook Air (Late 2008 or later), download and install Mavericks. Mavericks is a free update. You can check this site to see if you have any expensive software that would require updating first.

http://roaringapps.com/apps:table

I suggest you clone the drive first using one of these free clone apps.

SuperDuper! http://www.shirt-pocket.com/

CCC http://www.bombich.com/download.html

upgrading to Mavericks has a LOT of consequences.

research the abilities and features that are available in Snow Leopard, but no longer available in Mavericks - there are many - versus the abilities and features that are available in Mavericks but no in Snow Leopard (fewer).

If you have proof of purchase then an appointment with a genius at an Apple Store could help - they can reinstall Snow Leopard for you, and maybe give you some pointers too.

You will need to take the computer into the Apple store for help. You have no disks to restore and no Internet connection that is required to do anything further.

If it is indeed a 2011 model, it came with Lion, 10.7.x.

Restart and hold down the Command+Option+R keys to boot into Internet Recovery mode. Once at the work screen, use Disk Utility to erase the drive. Exit Disk Utility and install OS X. The machine specific version of Lion that Mac came with will be installed.

When done, the Mac will restart and behave as if no one had ever used it before and you will be able to setup the initial admin user account for yourself.

You do need an Internet connection to do this. Easiest would be to use an Ethernet cable and connect it directly to one of the LAN ports on your DSL or Cable modem.

Well, the good news is that there are no system disks to acquire because there never were any. A successful Command+Option+R restart proves that.

Apple's help page on the topic states:

Your computer's serial number is sent to Apple as part of this process to help authenticate your request to download and install OS X Lion.

Did you have a wired Ethernet connection from the start? Though that shouldn't make a difference to recognizing the drive.

Start again, only this time do a Command+R restart for normal recovery mode. Launch Disk Utility. Does the SSD drive show up in the left column at all? If it does, click on the physical drive name (far left indent) and then check the lower right corner of DU's interface. What does it say for the Partition Map Scheme?

Okay, that's why you can't install OS X.

Restart into Recovery mode. Launch Disk Utility and click on the physical drive again. Click the Partition tab to the right. Change the drop down menu over the graphic of the drive layout to anything other than Current. If one partition is all you want, choose 1 Partition. Make sure the format field to the right is Mac OS Extended (Journaled).

The Options button below that will now be active. Click that and change the radio button to GUID. Click Okay, then click Apply.

Exit out of Disk Utility. With a standard Ethernet connection to your router, you should now be able to choose the SSD and reinstall OS X.

You'll have to wait for the USB to Ethernet adaptor to arrive. Then plug the USB end into the MacBook Air, and the Ethernet end to your router. The Mac should then be able to access the Internet. I'm not sure what the adaptor looks like, so you may also need a standard Ethernet cable.