I ran into this issue as well, where none of the keys seem to work. I found that I could rebind the keys to something else and get it to work that way, but I couldn't get the game to let me change it back to CTRL+P. For me at least, the issue persisted after reinstalling TFAR.
On a potentially related note, I was unable to pull up a GPS as well, using RCTRL+M. Unfortunately, I've not had a chance to further investigate since I'm not at home with my desktop right now.