I recently removed my heatsink which has thermal tape on it to clean it out as it was stuffed with dust. Can I just put the heatsink back on with the old thermal tape and no thermal paste, just put it back on like it was before. I did this and now fear that I may have damaged the CPU. The computer turned on the first time and beeped continuously and would not boot, after that it just turned on and would not boot, it did not beep.
Im wondering if anyone has an opinion on what I did and if so did I ruin my CPU? I would like to know what to do next time just in case I did screw up. I have done this before with a P4 and had no problems.

Everytime you remove your cpu, you need to clean off the old thermal compound really well, and then apply new thermal tape/paste/compound.

The thermal compound is there for a reason...otherwise it wouldn't be a requirement. It helps to disipate the heat from cpu to heatsink. By using the old stuff, the contact was no longer 100%, and you introduced air bubbles.

Your P4 has thermal protection, and it will clock itself down when it overheats...which it's probably doing now.

As for your celeron, I don't know if they have thermal protection.

You should really read instructions and guides before playing with expensive equipment. By doing what you're doing, you're actually asking for your cpu to get burned (are you trying to get your parents to buy you a new cpu?)

No I can buy my own CPU. But basically the CPU is wrecked, thats what your trying to say?

Ok do I still have a chance of applying thermal paste and reinstalling the heatsink correctly and maybe it might still work. It ran for less than 1 minute all together, 3 times I tried to turn it on after I cleaned the heat sink. I knew something was wrong so I didnt turn it on again.

Well, it depends. You can clean it off really good, and properly re-install the cpu (by using new thermal compound). If it starts up and doesn't show any problems, then you probably didn't do damage (thermal protection via cpu or mobo).

If there wasn't any protection (again, most people use P4's, but I don't know if celeron has the same feature)...you might have possibly burned it out. (The cpu has a silver heatsink over it unlike a AMD chip, so you might not see it).

Only way to see if it's ok is to test it. Just do it properly this time.

Ok thanks I will give that a try a little later on. If not I guess Im buying a 2.93 or 3.06 Ghz Celeron to replace it. Thanks for the help.