I have a Gateway m675 laptop. When it boots up, I get an 02fa fan error, shut off computer and check fan. I installed a new fan, and get same error. I can't even bypass it. I did notice when I removed the old fan, there was a square of a dried substance, possibly thermal paste on it. The fan constantly runs when the computer is on or off. As soon as the battery is put in, they start, as soon as I plug it in, the fans start. The only way to turn them off is to disconnect the power supply and turn off. Any help would be appreciated.

Laptop fans are part of the CPU cooling heatsink assembly. The dried substance was probably dried thermal paste, as you noticed. This needs to be carefully cleaned off and new thermal paste needs to be reapplied. The fan runs constantly because the CPU isn't being properly cooled

use electronics cleaner/degreaser and clean thoroughly. Ensure the board is dry before powering. such cleaner evaporates very quickly, but is toxic. Clean in a well ventilated area.