ok i built my own computer back in april. it has held up more or less just fine until now....

1) recently it has been restarting without a reason, sometimes in the middle of a computer game, or while im listening to music.

2) after it restarted without an apparant cause it gave me a
"Bios ROM checksum error
detecting floppy drive A media...
Drive A error. System halt"

the whole time it gave off one steady beep, (or note?) rather since it didnt ever pause or break.

3) all of a sudden the picture just cuts out, i dont think its the monitor itself. The screen just goes blank and a solid single beep repeats every second or so. this happens at startup and during programs.

what on earth should i do?

That sounds very much like a CPU problem; heat. Have you checked the fan & or any noticeable heat?

BIOS ROM Checksum Errors:

http://www.pcguide.com/ts/x/sys/booterrGBER03-c.html

I also see fixes for this full error:
"Bios ROM checksum error
detecting floppy drive A media...
Drive A error. System halt"
recommending flashing the BIOS including the boot sector.

Also:

Change this setting to see if you can get an error message:

rt. click My Computer then click Properties then Advanced then Startup and Recovery Settings then unclick Automatically restart