Hi AES. I don't have the same scroll saw as you, but I recently had a failure on a bench-top milling machine which is electrically similar - a 500W brushed DC motor driven by a variable speed unit. In my case it turned out to be the motor (unlikely in your case) but I went through the logical process of tracking it down as it could have been the drive unit.
I have read your thread in the General Woodworking section and there is good advice there but here is my tuppence worth.
Firstly, as you have established that the drive unit is receiving mains voltage the fault is either in the drive or the motor. Because (presumably) the new fuse you installed didn't blow, the bang you heard probably means that something has shorted and gone open circuit. It's unlikely to be a rectifier capacitor or a motor winding in my opinion as the motor would still do something if only 'stuttering'.
In any case you're going to have to extract the drive board however painful the process - scraped knuckles and much cursing in my case! There will likely be spade connectors on the circuit board - make sure you label the wires/connectors and photograph before disconnecting (DAMHIK).
When you get the board out examine it for obvious signs of a problem - eg soot around components or a blown track. If there is something obvious you're in luck - the board has to be replaced or repaired, so some progress. In this case it would still be wise to check out the motor just in case a motor fault triggered a drive board fault. It shouldn't have but it's not impossible. If you haven't got a battery you can hook up to the motor as suggested earlier, it might be worth investing in a cheap multimeter (they can be had for under £5 in the UK at least) and checking the resistance between the brushes and between the brushes and earth as you rotate the motor.
If there is no obvious problem with the board you can check it out by attaching a 220V incandescent bulb (if you can get one!) to the output and see if it illuminates or (if you get a multimeter) looking for a voltage on the output.
Having said all that I'd put my money on the board having failed - it's the percentage bet - and suggest that if you don't want to get involved in the electrical jiggery-pokery you should just get a replacement board.
I should say that I'm not an electronics bod - this is just what I have gleaned from experience and research fixing my own machines.
Good luck, Bob.