Depends on partial or total failure of the transponder. If it fails in just transmit/receive, then 1. might be correct. Air to air coordination would still be impossible, probably causing own TCAS Fail annunciation, however. Actual performance may depend on the TCAS/transponder manufacturer.
A total transponder failure would shut off own aircraft altitude info to the TCAS, causing it to be inoperative, making 2. correct for sure.
GB