Highly doubt it will be because of a cap. A1200 can run with no SMD (except 47mf power ones) caps.
If it were a cap, it would have popped. You know when one of them goes pop, white smoke, bad smell and top will be missing or loose.
I would say, remove board from everything and have a really good look around the board. As yellow screen is CPU exception.
Check entire board (forget about Blizzard for now), there has to be something burnt up, if you smelt it. As BB already said, you may have missed smoke.
Could also be PSU, you got another to test, with just the A1200 mainboard (no Blizzard).
Is the 030 CPU socketed? I know most are. Have you tried removing this and reseating? Does the card also come with the optional FPU? Try removing this. Have had faulty FPU chips before now stopping systems from working.
For anything like SMD, the. It’s a case of probing and possibly desoldering and removal.
All the best.