I installed a new honeywell RTH7600D thermostat and connected the Red wire to the Rc terminal instead of the R terminal and left the jumper in as the manual suggested. Is it possible that it shorted out the transformer in the Furnace?

Because even thuogh I have correctly now connected the Red wire to the R terminal, I have no power to the thermostat.

I even re-installed the old carrier thermostat that was working before and it gets no power. When I move the thermostat upstairs, it works fine.

Any thoughts?

Very possible you`ve fried the transformer,, remember always any time fooling with tstats /or low voltage(24V) always turn off power to furnace