In the past I had a similar problem with my 3032 (2001N/32). I'm sure Dave will remember, since he and Mike_S helped me a lot with it.
I had a lot of problems... bad ICs, and a broken trace. I had the PET ROM/RAM board (
http://vic-20.de/x1541/hardware/petram.html) that helped me a lot to discovery what wasn't working, and an EPROM programmer that was absolutely the ultimate magic.
I discovered that, due a broken trace, the BASIC 2.0 ROMset simply didn't work. I tried the BASIC 4.0 ROMset and the computer booted with no problem. So, after thousand tests and ROM comparisons, I found the BASIC 2.0 hex code (few bytes) who prevent the computer from booting. Somebody here in the VCF told me what to phisically check, so I found the broken trace.
Before to ask help here, I spent about 10 years trying fixing it... I replaced *all* chips, and it still didn't work... But I needed some tools: the RAM/ROM board, and an eprom programmer. I bought the G540 Genius, a cheap, chines programmer who worth every single cent I spent. Currently it costs about 40 euros on eBay:
http://www.ebay.it/itm/New-Genius-G...986290?hash=item1c4531f572:g:tnwAAOSw3xJVXpdv
If you choose to buy an eprom programmer, don't forget to buy also an eprom eraser, they're cheap, about 10 euros.
http://www.ebay.it/itm/Ultraviolet-...632875?hash=item462aca9f6b:g:0pAAAMXQydtTOL7F
Too bad Nicholas Welte no longer offers its products (at least until some years ago he didn't answer emails), but it seems this guy is offering the same product:
http://blog.tynemouthsoftware.co.uk/2015/09/commodore-pet-rom-ram-replacement-boards.html
This board will replace all system ram and romset, so you can easily exclude two big source of problems. If you have some problem with ram or rom, the computer will boot. You can then choose to leave the board in place, or to chase the issue as I did.
You will need the eprom programmer to program the flash memory; in this case, I can send you the rom image ready to be programmed, I should have it somewhere, just post me in PM.
About wiring on the solder side: I don't know about 3032, but one of my two 8032 has some wiring, due to revision on the board. When I had to fix the other one, replacing the ROMset with the ROM image from the zimmers.net site, I had to make the same wiring mod, because it refused to boot with the new ROMset.
You could be in the reverse position: the wiring mod could be prevent the computer from booting with the new romset.
Take a look to that wires and try to see if they were made by somebody who needed to fix some bad traces, or if they were made at factory. In this case, maybe the new ROMset could be incompatible with that wiring mod. It's just a theory, but I think it must to be investigated.
At least, you have Dave on your side! LOL
Good luck.