That stuff is called heatsink compound which has many YouTube videos about replacing it.
And get a new fan as it sounds like it failed.
I have a dell studio 1458. I use windows 7 64.
The laptop was running slow lately and overheating even with simple tasks.
I thought I should clean the fan, so I disassembled the laptop. I was as careful as possible. I did it all in a very organized way to avoid getting lost with the screws or matching the cables on the right spot.
After all the process, I cleaned the fan. It was really dirty...
( I don't know if this is important, but there was some type of gum between the processor and a piece of metal connected to the fan. That gum was very thin over the processor, so I slightly reshaped it to give more 'cushion' between them)
... After cleaning the fan, I asambled everything and turned on the laptop. It worked great for some minutes. The fan was very loud, but I assumed that it was because now it's working properly.
However, after 10 minutes, the laptop stopped working. If I try to turn it again, it automatically turns off in a couple of minutes.
Please help me. What could be the problem? I can't afford a technician So I want to solve it with my own hands.