My start up disk is full

Do not ignore that message. When that occurs your Mac has exhausted a number of increasingly desperate measures to free the minimum amount of space so that it can continue to work. If you continue to ignore those messages you may not be able to boot your Mac at all.

Read OS X Mavericks: Increase disk space.

Resetting NVRAM could solve the problem.

I'm confused. You wrote that you deleted several documents as well as over 6500 photos and videos but you are asking how to delete files. Are you still encountering that dialog?

Rebuild the Spotlight index: Spotlight: How to re-index folders or volumes - Apple Support

By resetting the NVRAM will I lose everything on my computer?

No.

You deleted photos and videos?

Were these photos and videos you wanted to keep? If so, do have have a proper backup of all your photos and videos and if not, whatever you delete is permanently gone.

You shouldn't be just deleting items willy nilly. Especially if you have no backup of any of your important data.

Here are some of my general tips to keep your Mac's hard drive trim and slim as possible

You should never, EVER let a computer hard drive get completely full, EVER!

With Macs and OS X, you shouldn't let the hard drive get below 15 GBs or less of free data space.

If it does, it's time for some hard drive housecleaning.

Follow some of my tips for cleaning out, deleting and archiving data from your Mac's internal hard drive.

Have you emptied your Mac's Trash icon in the Dock?

If you use iPhoto or Aperture, both have its own trash that needs to be emptied, also.

If you store images in other locations other than iPhoto, then you will have to weed through these to determine what to archive and what to delete.

If you are an iMovie/ Final Cut user, both apps have their own individual Trash location that needs to be emptied, too!

If you use Apple Mail app, Apple Mail also has its own trash area that needs to be emptied, too!

Delete any old or no longer needed emails and/or archive to disc, flash drives or external hard drive, older emails you want to save.

Look through your other Mailboxes and other Mail categories to see If there is other mail you can archive and/or delete.

STAY AWAY FROM DELETING ANY FILES FROM OS X SYSTEM FOLDER!

Look through your Documents folder and delete any type of old useless type files like "Read Me" type files.

Again, archive to disc, flash drives, ext. hard drives or delete any old documents you no longer use or immediately need.

Look in your Applications folder, if you have applications you haven't used in a long time, if the app doesn't have a dedicated uninstaller, then you can simply drag it into the OS X Trash icon. IF the application has an uninstaller app, then use it to completely delete the app from your Mac.

To find other large files, download an app called Omni Disk Sweeper.

http://www.omnigroup.com/more

Also, Find Any File

http://apps.tempel.org/FindAnyFile/

Typically, iTunes and iPhoto libraries are the biggest users of HD space.

move these files/data off of your internal drive to the external hard drive and deleted off of the internal hard drive.

If you have any other large folders of personal data or projects, these should be archived or moved, also, to the optical discs, flash drives or external hard drive and then either archived to disc and/or deleted off your internal hard drive.

Moving iTunes library

http://support.apple.com/kb/HT1449

Moving iPhoto library

http://support.apple.com/kb/PH2506

Moving iMovie projects folder

http://support.apple.com/kb/ph2289

A disclaimer,

Things to consider before moving your iPhoto Library Folder to a new or external location like an external hard drive.

If you make movies on any iDevices using iMovie for iOS,, then transfer the video footage, the IOS version of iMovie saves the footage as a movie file in IPhoto for IOS and will automatically get transferred to iPhoto for the Mac when you upload the video from your iDevice.

Newer versions of iMovie will work and link those video files found in your iPhoto Library on your Mac, but those links can be lost if you move your iPhoto library and you will not be able to relink that video afterwards as the current versions of iMovie seem to not have a relink option for the video portion of the files (ironically, current versions of iMovie HAVE the ability to re-link the audio files from the video footage, though (The inability to re-link the video files could be a possible bug or oversight in current versions iMovie).

The lost video links show up as "blacked-out" video blocks with no content.

Before moving the iPhoto Library

If you make movies with iMovie using iPad or iPhone video then 'Consolidate' the files before you finish. This will gather (albeit by duplicating) all the relevant files in the project in one place. After consolidating/duplicating all of the audio and video footage to a seperate, independent location,it should be safe to move your iPhoto library.

The potential way to circumvent this issues maybe to try and import iPad and iPhoto video directly into iMovie which would be another solution.

Get started using a proper local backup strategy, too.

Backup your current system to an external connected and Mac formatted Flash drive OR externally connected USB, Thunderbolt or FireWire 800, Mac formatted hard drive. Then, use either OS X Time Machine app to backup your entire system to the external drive OR purchase, install and use a data cloning app, like CarbonCopyCloner or SuperDuper, to make an exact and bootable copy (clone) of your Mac's entire computer system and data.

Good Luck!

Did you empty the Trash after deleting the files?

Disk Space - Other