Beeping laptop power supply HP

My HP laptop power supply has failed and just beeps repeatedly, initially I just had to tap it on something a few times and it would start working again, but now that has quit working. I've taken it apart and its full of some kind of silicone gunk. The pesimistic side of me says thats to prevent people form fixing them, but I'm sure its to absorb shock and prevent shorts. My first guess is that it's a relay near the AC power plug because the banging things on it caused it to work for a little while until power was turned off. There are two large inductors on either side of the relay and two large 120v caps below that. Then a transformer and a set of smaller caps below that. Three higher voltage transisters around the edges. The other side is littered with surface mount (I didn't realize it took so many parts to make a power supply) I am unable to find anything that looks like a fuze unless its the part rapped in heat shrink but its upright with the leads coming off the bottom and only about 2mm diameter, 5mm tall. Its really hard to see with all the silicone gunk and I shocked the crap out of myself repeatedly until I cut enough silicone off to discharge the caps. I'm unsure of how I want to proceed, I guess I'm just searching for a multimeter and hoping my roomate has one. If I figure it out I'll try and remember to post it. The pesimism in me (again) feels that they are designed to fail at a week point.

I'd like to find some ways to fix this problem since it seems to be fairly common. I know my issue is with the power supply and not with the laptop as some people have experianced. I am only interested in fixing it, buying a new one is the obvious solution but I'm fairly certain this is a simple fix.