It looks like the Homepin fellow has been scathingly critical of the original board design:
https://www.aussiearcade.com/showth...ttack-From-Mars)-STROBE-board-PROJECT-STARTED
With those criticisms and your lack of success despite all the replacements, it looks like these boards are right bastards.
Just for sanity's sake, there's definitely 50V AC, and +12V DC coming from the power driver board in the backbox to the strobe PCB, right? J1 pins. Check those with the strobe board disconnected and check on the cable that connects to the board, just to rule out any issues earlier in the pathway including cable. Checking the cable is a lot safer than trying to test any point on the board, as the other guys said, death voltages in this circuit but the cable is just spitting out 50VAC, which is marginally safer.
Now, assuming the board is getting power... I'm a bit **** at circuit designs, but in my worthless opinion looking at the schematic, Q1 being dead definitely accounts for the board working - but C1 not exploding when fed a polar resistor seems to be luck as it it's still exposed to alternating current without Q1.
As for a replacement for that capacitor - there is a like-for-like on ebay, it's ridiculously priced for one capacitor of this type IMO but the only place I've found to get this sort of thing cheaper is to go to the wholesale electronics guys, like mouser, farnell etc and the delivery charge they will apply makes it more expensive than this, it's only economical from those places if you do a big order -
https://www.ebay.co.uk/itm/CEB-100-...802602?hash=item1a387c092a:g:riMAAOSwc6pZ8Htl
The other option is to take two classic polarized capacitors (like the ones you used) and solder them in series, in same poles to each other. Negative-to-negative or positive-to-positive, it doesn't matter to the circuit which you do. It's theoretically absolutely sound but it will probably feel really dicey and you'll have to get creative in where you stick the buggers on the board.
https://electronics.stackexchange.c...tic-capacitor-out-of-two-regular-electrolytic If you do this I recommend heeding Mike (Homepin)'s advice and using 160V caps for the job instead of original 100V