Hi Felix,
The main problem when beginners troubleshoot electronic stuff is the foreknowledge and test equipment that you need to do it. For a one off repair this is just not cost effective, unless you are going to take up electronics as a hobby as well.
My suggestion would be to try and find one of those old fashioned TV/PC repairer shops and having attached a light bulb instead of the motor have them look at it. Finding a circuit diagram to put with it might save you money.
OK, so if you want some tips to try anyway…
Remove parts, one by one, from the PCB and then test them with a DMM, as often the circuitry and other failed parts can make good parts look bad.
In your case where you have a fuse blowing. Remove the MOSFETs and test them, also see if it still blows the fuse with them removed. The idea of connecting a lamp as a load while testing is really good. If you suspect the bridge rectifier remove it as was done with the MOSFETs and see if the fuse still blows, etc.
Don't forget that circuits like that you are troubleshooting are are often at mains voltages and have risks to your health…
Bob