Put your original stick back into slot 1, and then the donated stick into slot 2 as you've been doing and then try and reset your BIOS. Easiest way to do this is to take out the small circular CR2032 battery for approx. 30 seconds and then put it back in. Saves fiddling around with small jumpers....
If that doesn't work, then try both sticks in the other machine. If both sticks work together fine in the other machine, then it looks like you have an issue with the motherboard on the machine you want to continue using.