Yes! I agree with what BarakandI said - the wiring looks to have been fanagled with so compare it to the drawing he included. And extremely important -- add the fuses!
https://www.pinwiki.com/wiki/index.php?title=Williams_System_3_-_7#Additional_Fuses

The blue wire going to BR1 is burnt. That is one AC leg from transformer. Second blue wire to BR1 is MIA, was apparently replaced by somebody with a yellow wire. Yellow may also be burnt since it looks a bit deformed at the top loop.
Take note of where the wires are, pull the quick connects from BR1 and test BR1 using a meter's diode test function. I'm leaning towards a shorted bridge rectifier. If so, replace with a GBPC3504 or GBPC3504L.

Before you power it up again - get yourself a couple inline fuse holders (e.g. Littelfuse 01550100Z) and 8A fuses and install them at the red "X" locations:

Fuse_Me (resized).jpg

With the mess in the wiring - do yourself a favor. Remove the mess that somebody put in there and rewire it properly.
Two new blue wires from transformer to bridge rectifier.
Two new red wires from transformer to bridge rectifier.
Add two new fuse holders and 8A fuses.
New violet wires from bridge rectifier to cap and connector 3P1.
New black wires from bridge rectifier to cap and connector 3P2.
New faston connectors (or solder direct to bridge).
New contacts for connections at 3P1 and 3P2.
Maybe new bridge(s) for BR1 and maybe BR2.
Maybe secondary side of bridge rectifier BR2 as well.

Wire size - depending on overall length of wire:

Fuse_Me_Wire_Size (resized).jpg

Or better ones here:
https://www.greatplainselectronics.com/proddetail.asp?prod=GBPC3504L

Leave the transformer in place (unless you can't reach the backside of transformer), you are only replacing the red and blue wires that go to lugs (solder points) on secondary side of the transformer. It takes a bit of heat to get the solder flowing on these so take your time.
The photo within post #1 shows the primary side of the transformer, opposite side not shown in photo is the secondary side which is where you would be replacing the wires.

Lugs #11 and 12 for lamps (blue wires), 13 and 14 for solenoids (red wires).

The transformer in photo of post number #1 actually looks pretty good. Only thing I would do is pull that brown primary wire away from lug #7 so that the lug doesn't chafe it's way through the insulation. And - in same photo, there appears to be a loose bit of wire under transformer that should be pulled out.

An option to inline fuse holders is to add a couple fuse blocks to the right of the two bridge rectifiers.
Here is an example for the fuse block:
https://www.greatplainselectronics.com/proddetail.asp?prod=354001GY

Oh, shit...

Yes, that would work.
But heat slug bridge rectifiers (phenolic body, metal top) have lower thermal resistance (lower is better) than full metal body bridge rectifiers.