I'm not quite sure what you mean about the two 7805's...if you mean they are both connected to ground at the same point and both connected to your unregulated power supply, then that's ok...but if you have one of them connected to the unregulated power supply...and the other connected to the output of the first one, then the second regulator won't work properly because it's input voltage will be too low. Also make sure you have enough decoupling on the input and output of each regulator, otherwise satbility problems will arise...
The PC not receiving the characters, or more likely not displaying them, is probably down to a software problem. Check your data tx line on your board to see if it is or isn't sending when you expect it to.