Today I purchased a memory module for an older laptop (Model No. Compaq Presario 1500US). The module I purchased was a 512mb Corsair Value Select DDR-266mhz stick.

When I put it into my laptop's free slot it booted fine and worked for three hours. When I rebooted it, however, it displayed the windows loading screen with the blue bar, and then immediately bluescreened and rebooted. The STOP error is displayed for a fraction of a second, so I can't read any information on it (Unfortunately)

I tried rebooting with only the original stick in and it got the same error. Same thing with only the new module, and the same thing when I tried safe mode.

Do you think this is a memory issue or could it just be that my 7 year old machine has just given up the ghost?

It needs and will only use the DDR PC2700, which I would guess is 266MHz... You should have two modules of 512 mb... I would run them one at a time to see if one of them is bad... or else run MemTest86 for four hours or seven passes which ever is longer, one module at a time, to assure that one of the modules is not bad.
New memory can be bad, just like old memory can.

PC2100 is what the original stick that was in the computer said so that is what I purchased.

The ram stick however isn't bad. I put it into another laptop and it ran and booted fine.

The error message I am now getting (on the old one) reads UNOUNTABLE_BOOT_VOLUME

Thanks for the reply though

It appears you have a failed or failing hard drive.