What makes you suspect that it is the CPU, as opposed to any other component?
I'd follow Beta's advice to make sure, but normally you just leave the disk in but DO NOT press any key when prompted to boot from the CD after the reboot since you are already past that stage - it just needs to finalize the installation by that point.
Also check in the BIOS to make sure that the hard drive is set as a bootable device.
If there is a hardware fault, it sounds more like a hard drive or motherboard fault as the computer seems to be struggling to find a bootable partition on the hard drive, although I'm inclined to think that's not the case. If it was a faulty CPU I don't think you'd even get past the POST stage.