This stuff is probably not a problem:
That is most likely a sort of glue used to keep the parts from moving around.
This stuff probably is a problem, though not the cause:
Those resistors appear to have burned. If so, they are no longer OK. They are not, however, the cause of the problem. Something else went bad and caused too much current to flow through the resistors. That something else is the cause - and it may be something you can't see just by looking.
It can probably be repaired. Whether a novice could do it or not is a toss-up. Maybe, maybe not. It depends on how much time and effort you can spend
on it. It also depends on how careful you are. That circuit works with the AC line voltage - making live measurements would be dangerous.
Philips probably sold a replacement at some time. Whether they still do is something you'll have to discover on your own.
There's a service manual available here.
These are the burned resistors:
Most likely, Q2 has failed short (it is short circuited inside.) It may have simply failed, or the driving circuitry may have failed.
You'd have to check and replace Q2, maybe also Q1 and Q3. You'll also need to replace those burned resistors. You might also have to check transformer T1 - if it is shot then you'll probably have to give up because it will be custom made. There's a fuse where the AC power connects to the board. It should have blown when the resistors burned out - that's probably the pop you heard. You'll need to replace it.