Cooling fan running, but computer shuts down

Recently my laptop fan seemed to be running harder (louder) and when on the internet the computer would just turn itself off. When working off line the fan was still noisier than it used to be but it would not randomly shut down. I vacuumed out the fan although it was not that dirty and checked inside, but all was clean. Now it shuts down within minutes of turning it on, whether online or not. It seems as though its a thermal shut down due to the fan running hard, but it hardly has a chance to heat up. It's a Dell, running Windows 7 and has had the hard drive replaced several years ago; other than that its had no problems.
 
The thermal paste or grease under the fan's heatsink dries out over time, causing the laptop to overheat and shut down quickly. Noisy fans and thermal paste can be replaced
 
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