I have a 2010 Jeep Wrangler. I purchased a new alternator and it's still not charging. Does the TIPM have something to do with this?

If you have access to a good bi-directional OBDII scan tool, you can do a functional test on the PCM alternator to see if it's receiving and sending a signal to and from the alternator.
Chances are that the PCM is most likely at fault. The 2010 Jeep Wrangler PCM is notorious for alternator failure which means the PCM has to be refurbished.
 
The TIPM is much less likely at fault but could be a culprit if especially if you find any signs of corrosion on the pins of the TIPM and wiring harness plugs that connect to it.