Want to replace the old analog thermostat on my Carrier HVAC with Bryant handler and heat. It appears that the original installers cut-off the blue wire thus making it a 4 wire thermostat with I assume no common. Want to replace with Honeywell TH8320 with a common so it will operate on power not batteries. Any ideas on how to 'correct' this without pulling a new 5 wire through the walls? Many thanks.

Splice the blue wire if you can get to it.

Thanks. I think there is enough blue wire in the thermostat bundle to use. My new situation appears to be at the Bryant air handler. The wire from the thermostat comes through the closet wall and attached to a terminal board on the side of the air handler. There are 5 screws there labeled, Y,G,W,4/R and X/F. Only 4 wires of the house wire are visible with the yellow connected to the Y,green to the G, white to the W and red to the 4/R. I do not see any blue wire on this end of the thermostat wire. It appears that the 1976 installers just cut off wires they didn't not need or use. There is also a short segment of thermostat wire running from this same terminal board to the bottom of the compressor unit. Two wires here; a red wire connected to the X/F terminal on the air handler and a white wire connected to the Y terminal along with the yellow wire from the thermostat. I have found internet pictures of this same old thermostat but the terminals in mine are labeled differented. For instance, mine is G-F instead of G, Y-C instead of RC, 4-M instead of Rh, RV instead of Y, and W/H instead of W. Any help in determing what terminal could/is be used as the 24V common will be appreciated. I certainly don't want to have to run this new TH8320 solely on battery power.