I would definitely recommend getting the game running properly before attacking the fuse-blowing problem. First, you want to make sure you have good voltages. 5v, 14v, 43v, etc all need to be within spec or else you're going to waste lots of time and patience trying to track down intermittent (or not-so-intermittent) problems. Chances are you're going to need to re-pin some connectors, re-flow the solder on the headers of numerous boards, and then see where you stand. You'll also want to replace any/all electrolytic capacitors on the boards, particularly the power supply board. Worst comes to worst, a new power supply board is available here: https://ksarcade.net/swemmer-6803-power-module.html
In my opinion, the original boards are usually fine, they often just need a bit of freshening up (new caps, reflow connectors etc), so I'd definitely try fixing what you have before ordering up a new one.
I would start by measuring voltages at the various test points. I copied this section from pinwiki's Bally 6803 guide, which is here: http://www.pinwiki.com/wiki/index.php?title=Bally_6803#Fuses_and_Test_Points5.1.1 Fuses and Test Points
The following table lists the circuit protection fuses for each circuit on the power supply.
FU1 - Solenoid Power - 5A SB (2 flippers), 6ASB (3 flippers), 7ASB (4 flippers)
FU2 - Display Power - 3/4A FB (a 3/4 inch fuse from the factory...suggest revising the power board to accept 1.25" fuses)
FU3 - 5V Logic Power - 6A SB
FU4, FU5 - 20VAC Controlled Lamp Power - 8A SB
FU6, FU7 - 6.3VAC General Illumination - 15A FB
The following test points are available on the power supply.
TP1 - 5VDC
TP2 - 190VDC, adjustable via the trim pot
TP3 - 230VDC, unregulated
TP4 - 43VDC
TP5 - 14VDC, unregulated
TP6 - 11VAC
TP7 - 11VAC
TP8 - 6.3VAC
TP9 - 6.3VAC
TP10 - Ground
I would recommend using TP10 as ground for reading the DC voltages. Jot down your findings and report back. Also make sure you have the correct fuses installed (rating and fast/slow blow type).