My 2003 Infiniti QX4 shifter cable melted @ shifter, damaging cable not allowing me to shift into park or any other gear. I had car towed &Replaced it. now the transmission will not shift into park or any other gear.

Without seeing it, it would be hard to say. There could be additional damage from the melted cable. Could be installed improperly or adjusted wrong. There are several other issues external and internal to transmission that can cause this. I would take it back to the shop that did the work or some other reputable shop to have it evaluated.