In a sense, I admire your fortitude...especially if it is successful. Would you mind of I asked some questions?
First, can you offer up the name of the unit as in a model number or anything similar that might give everybody an idea of the details of its operation. A schematic exists somewhere. I read through the thread and see no such reference.
There could be a wealth of information in the manual, especially if there are some built in diagnostics which could be implemented with the little tone generator.
Are there no sensors on the unit? I would expect that there would be associated with freezing and thawing. It could be programmed to not operate the fa or pumps without valid sensor input.
You received it from a friend as "faulty". Can you provide any other information on that? For example, was it ever working? Did some event occur, after which, it became faulty? That kind of thing.
Did you verify good quality +5 and +12 power?
If I understand correctly, you removed some transistors from the board. How are they marked and have you tested them now that they are off of the board. They may simply be drivers for the PIC to operate the relays, but you have an opportunity to evaluate them separately now.
You said that the PIC gets hot - did you mean warm or too hot to leave your finger on the chip?
....just some thinking