The first thing to try is to take some 99% isopropyl alcohol and your roommate's toothbrush and scrub the mess off.
Tilt the board so the alcohol and suspended mess will run away from the dirty IC's legs. Dip the toothbrush in the alcohol. Hold a piece of paper towel against the PCB, below the last of the corrosion, to catch the goop that will run off and scrub the legs of the IC in the direction of the legs. Scrub the other contaminated areas below the IC also. ReDip the toothbrush in more alcohol and repeat until it isn't getting any cleaner. Blow out any alcohol that may remain trapped under the IC. If the pins are still all attached to the IC and the traces appear intact, then you can try and see if the laptop still works. If not, you'll need to remove the IC, clean under it, inspect the traces under it and replace the IC if the traces are OK.