posting beeps with a bad cpu depending on the board is hit or miss so basically you can't depend on it.
I also could not find any info on the red light at least not on the intel website.
Did it ever have video with the new psu?go here
for some tips from intel, pay special attention to using the correct power supply:avoid no boot/lock ups.
If you remove the ram and power on, do you get any beeps, if so this usually indicates the mother board is good, if not remove all cards and drives and try and get into bios if you can get into bios the it would be a bad drive or card, if not it would be the ram, mobo, cpu or psu. So if you could try different ram that would eliminate that, then if you could try a known working psu that could eliminate that.
All that would be left would be mobo or cpu hard to tell witch but when a board won't beep my 1rst guess is always the mobo.