iMac starts, shuts down - gray screen w/ progress bar

I have a 2007 iMac and it is now shutting down every time I try and restart it. I see a gray screen with the apple logo, the spinning wheel and the progress bar upon every restart. The progress bar never finishes and it shuts down.

I have restarted with command-option-P-R - same result

I have restarted with command-S - same result

I have restarted with command-C - it kept spitting the disc out then it would shut down again

I have restarted with command-V and it said something about incorrect block counts. It also at the very end, just before shutting down again said "Disk Full Error" and "killing all processes done". I had to snap a picture with my phone to see what it actually said since it happened so fast. I knew the hard drive was almost full and was actually backing up to and external hard drive just before this issue began.

Is there anyway for me to force the computer to stay on long enough for me to remove some items and free up space? Like an override somehow?

Thanks so much in advance for the help!

Shayna