Here are links to a couple of documents that might help.
First is a mini lathe troubleshooting guide:
The other one has details about the motor controllers used in the Sieg X2 mini mill, including photos and schematics - IIRC the same or similar motor controller is used in the mini lathe:
Although the photos that you have posted do not look identical to what I see in those documents, so maybe none of this will help.
The author of the second document (Gerling Laboratories) has a business that repairs similar motor controllers, and perhaps his web site will have some useful tips:
The "KBLC-120" board pictured at the bottom of that page looks to be the same as the board that you have pictured, with several transistors lined up along a common heat sink.
If I do a google search on KBLC-120 it brings up pointers to sites about a KBIC-120 controller which may be the same thing. For example, see http://www.kbelectronics.com/data_sheets/kbic.pdf
But maybe there is in fact a KBLC-120 as well (if I force google to search on KBLC-120 instead of KBIC-120) - see http://www.kbelectronics.com/manuals/kblc.pdf
When I looked for info on the KBLC series, though, I ran across the following statement: "KBLC-120 & 240 - See KBIC Series Drive Installation & Operating Instructions". So maybe the KBIC link above is what you need.
Also maybe the "motor test tool" on the previous site might be useful:
So, my apologies for the stream-of-consciousness reply, but chances are that somewhere buried in this stuff you will find your answers...