I hooked up my new honeywell RTH230B thermostat and the heat seems to be working, but the airconditioning won't come on. I hooked the W to the W, the Y to the Y, the G to the G, the R to the Rh and the C to the Rc. At first I tried it without the jumper between Rh and Rc because that's what it said in the instructions, but I also tried it with and it still didn't work. Any suggestions?

C is a newcomer to the thermostats. It wasn't required on the older ones. It is required when the thermostat does not relay on batteries for the primary power. C has to come from the opposite end of the transformer that R was connected too.

You need to run a wire for C.
Rc gets connected to Rh which gets connected to R. c and h refer to heat and cool. Using Rh and Rc accommodates two transformer systems.

The reason why your heat appears to work is probably because of some backfeeding of power.

I unhooked the C wire, hooked R to Rh and jumped Rh to Rc. Now neither heat or cool is working. Could I have blown out a fuse or messed up my thermostat by hooking it up wrong to begin with?

C was on the old stat. I missed that. Saw it after I looked up the instructions. (C) needs to be taped so it doesn't hit anything.

Some furnaces have fuses on the control transformer. Others do not. You could have damaged either new stat or transformer.