RAM would only really make a computer faster, if 1, the speed of the RAM was faster than the previous set, and your motherboard supported it, or 2, your computer was struggling to run everything at once with the limited amount of RAM.
If you get the same speed RAM, when for instance you have 2GB's, and your system isn't reaching the entire 2GB's limit when in use, installing an extra GB, or 2GB's won't infact speed up the PC, since the computer wasn't using the extra available RAM in the first place.
In your case, if after installing the RAM, the computers going slower, then yes, this seems like a fault with the memory itself.
There is an updated version of Memtest called RAMProbe:
You need to create a bootup file of the program though, either with a floppy, or CD drive (I think). I'm not sure if a bootable USB stick works if thats also an option.