Inspiron N4010 processor

around April, my laptop started experiencing issues where it would bog down, and sometimes completely shut off.  After trying to run diagnostics several times and not even being able to get through that, I opened it up and found a giant dust bunny clogging the fan.  After removing that, the shutting down issue seemed to go away, but I would still have periodic issues where the processes would jump to 100% and I'd pretty much have to close everything down.  We're talking maybe 1 Google Chrome issue, iTunes and Skype - all applications that this laptop should be able to handle running simultaneously.  I tried removing and reinstalling java and flash, but to no avail.   Sometimes I didn't even have a browser open - I might just have iTunes and Skype - and it would shoot to 100%.  I ran all the various diagnostics and virus scans and the only thing that ever comes up negative is that my battery is near the end of its life.  But I've even tried running it without the battery and it still has the same issue.  I was going to try swapping out the hard drive so I could run a clean Windows install, but the hard drive is not one that is easily removed, and I wanted to be able to put my normal hard drive back in if necessary, so I avoided that.  I did get the replacement hard drive in (with nothing loaded) and ran diagnostics and experienced the shutdown a few times with that, so I'm pretty sure it's not the hard drive.  I finally pulled everything out, and when I got to the processor, I noted that there is a thin layer of perhaps insulating material that is pretty much gone:  

There is another chip near the processor that has a similar layer that is intact:

I'm wondering if this could be the root of my issue, and if so, is there something I can use to recreate that layer?  A small square of electrical tape?  Maybe cut a square from some old cable insulation?  Or do I just have to replace the processor at this point?

Thanks.