I have a small tower Dell Optiplex GX240 that only accepts one GB of Ram. Can I put in another motherboard that would allow more memory and more power?
If you are going to replace the motherboard you might as well just replace the whole system, a board to support the old P4 CPU in a GX 240 isn't going to be cheap, and you are going to need a new case because i believe the GX240 only supports 1GB because its got 2 memory slots and is using DDR not DDR2, so you would need to move up to a full ATX board and change cases. When you swap the board the OS won't be able to load anymore since the drivers will be different, you will need to reinstall windows but will need a different copy since the one on the hard drive is tied to the dell motherboard.
Anyway, its too much work to bring a GX 240 up to the modern era, a cheap prebuilt running an i3 will be significantly more powerful and won't cost you too much more than upgrading that GX240 would.