2 likely possibilities:

1. Flipper relay coil is fried.
2. Driver circuit for the relay coil is fried.

Check your manual as to which transistor on the Solenoid Driver Board drives the relay (one of the big ones on that run along the bottom of the board).  With the cardboard out, ground the metal tab of that transistor with a jumper wire.  If the relay pulls in, the transistor (or something else upstream) needs replacing.  If it does not pull in it is most likely that the relay coil is gone (but check the tracks leading to the relay for damage and resolder the relay pins just in case it is a dry joint).

Hope this helps!
Ian