Okay, my computer is very clogged at the moment and I would like to do a complete restore, but I have some files that I need to keep. Is there a way I can do a complete restore but keep some of the files (no external hard drive).
In a word, No.
If there are any files you need to keep, transfer/copy them to a USB drive, CD/DVD/disc or another disk drive.
Doing a complete restore and in a sense, you'd be doing a clean install, you will loose all programs, files, etc: that you installed.
I know that's not what you wanted to hear, but, it is what it is.
Add to the former, it's quite smart to have your personal and important files on a separate disk, or at least a separate partition. It's inevitable that you need to re-install Windows one of these days, and having your own stuff in another place than your OS will secure them, as well as give full liberty to wipe out the system disk in order to make a clean install - this could also become actual if your computer gets infected by a virus, leading to a possible and total shutdown --- your personal files will be safe. Attacks usually head for the OS.