Every time I try to start Blood, I get this error.
It seems to be from Blood not starting through dosbox and instead trying to start through CMD, but I can't seem to make it run through Dosbox as I have no idea how and the tutorials I found on the internet didn't seem to work (One was for Ubuntu and the one on the wiki wasn't even there.)
Specs:
Windows 7 Ultimate 32-bit
AMD Phenom 9850 2.5 Ghz Quad
ATI Radeon HD 5750 512mb
2GB DDR2 RAM
I ran the game before I upgraded my processor fine (Same OS, Ram and Graphics card) so the problem may stem from that.

Have you tried reinstalling the game?

Yes. Didn't work.

Are you running blood.exe or are you running the link to dosbox.exe? Right click the icon you are using to launch the game and select properties. That should tell you.
You should be running dosbox. This will invoke the emulated DOS environment that Blood needs to run in.