j
I'd definitely give a little repair shop a try.
Looks like just maybe it's the transistor(?) down in the lower righthand corner of the first photo? I've removed and replaced leaky capacitors on power supply boards to good effect, but that's because the capacitor itself had failed and wasn't caused by anything else. If that's all it is, you could order one online for a few bucks and solder it on yourself.
The component should have more numbers written on the black shell that you might be able to check online for. Not necessarily on the circuit board, but tiny hard to read type on the piece itself, unlike the resistors etc.
Good luck, whatever it is!
saturn
the transistor is a likely point of failure, but, by no means the only one
points of high current flow often go bad, causing the need to resolder "ringed" solder connections. caps develop high ESR, driver transistors fail, that little high frequency "chop" transformer could have an open winding...
i wish i recognized the laminator the reverse engineering people copied. the chinese are great at this, but they often skimp on the parts that make building the device expensive
someone posted that it looks like a GFP 563H
i will see if i can acquire thecservice manual, although if he only neds cold lamination, I could do that with a dc power supply and a clip lead
if he were in the US, i would have ups'd him something to try