PC not running for more than 15 minutes after cleaning CPU fan

This might be a hardware problem.

Enter BIOS setup, wait a minute or two, and see whether the fan keeps spinning. If it doesn't, you probably have a hardware problem.
You can also try booting to a CD (eg, Knoppix) and see whether it stops spinning.

1. The computer can't detect the sensors
   The computer may run the fans at full speed if it cannot detect the temperature of the cpu. If there are multiple sensors and one is not reading there is also chance that the computer has fallen back to its failsafe. It's better to keep a processor cool than let it get too hot and not know about it.

   (I remember fixing a mac a few years back which had a fan running at full speed constantly - and though it is a mac, it could be the same problem as yours.)

2. The BIOS settings are wrong
   I don't have much experience with BIOS settings, but do check to make sure you haven't changed a setting accidently which is causing the fan to run at full speed constantly

3. Are the sensors faulty? It's an unlikely one, but it is still a valid point to make because you have been fiddling with the hardware and could have caused accidental damage. Check the sensors for physical damage and grab yourself an application for monitoring fan speed (I use speedfan, though it doesn't work for all systems.) and see if any sensors are showing odd numbers

The only harm you're likely to sustain having the fans stuck at full speed is premature motor wear, excessive noise and increased power consumption (though it's a laptop, so this extra power won't be any more than the battery can handle).

Failing all of this, it could be an issue with the operating system (on systems where the OS controls the fans) or the BIOS (on systems where the BIOS controls the fans). Any damage could have been caused if you forgot to ground yourself to a piece of metal before working on the inside of the laptop

I hope this answers your question