|"Processor runs continuously but no display"|
I'm fairly sure the processor IS working because if it wasn't, there would be no beep codes. But I'm curious how you came to the conclusion that it "runs continuously"? Just because the CPU cooling fan is working?
Anyhow, you didn't list the make/model of your motherboard or which BIOS it uses (AMI, AWARD, Phoenix, etc). Each BIOS manufacturer uses different beep codes. I'm going to take a stab at it & guess that you have an AMI BIOS. 3 beeps = memory error.