The card appears to be in good shape, of course that doesn't mean too much. But there are no obvious signs of damage, blown caps, etc. Any suggestions for things to check or try?
Assuming the TWGS is set to its default settings, when it boots, it will display the animated TRANSWARP GS logo, with whooshing sounds as it splashes on the screen and then disappears. Sorta like this:
https://www.youtube.com/watch?v=g5FOMiMwN40
The socket on the GS motherboard is pretty sensitive to the number of extractions/insertions. The pins on the factory TWGS cable are very brittle (unless it came with an improved replacement cable). GENTLY spread the pins on the cable apart, and carefully re-insert it into the socket. We're aiming for optimal socket contact. Try that first, then we'll investigate other possibilities.
Edit: better one - https://www.youtube.com/watch?v=39L4pBRRBCs