Heat Pumps and Electric Heating - Bryant HP problems

Been having a nagging problem with my Bryant HP. Let me start from the beginning. Back in the summer of last year it would not come on at all. Sercive man came out and checked it out. He said it was the t-stat. It was the builders digital t-stat from Bryant. The service man then put in mechanical t-stat. Unit worked then quit again. Come to find out there was a wire that was broken and would sometimes make contact. So he used a spare wire in the bundle. Afterwards we did not have any problems for the rest of the summer. Now, it's winter and finally using some heat every now and then. BTW, this is Baldwin County Alabama. Now the unit will come on when it gets below set point and heat the house. Then when it gets back to set point the inside fan will conitnue to run and the outside unit will shut off for about 30 seconds and then kick back on for about 30 seconds. It will continue to do this untill I move the set point way down or put it in the off position. I changed the t-stat out and installed a Hunter HP programmable t-stat. It seemed to work fine for a while and is now having the same problem. Never had this problem before we had to call the service man. Any ideas what it may be? If it's a card can I buy one from somewhere or will an AC contractor have to buy it?

Thanks,
Steve

I did find out that it is not the circuit board. Robbed a board from a vacant house down the street. Same unit and board. Swapped the boards out and still no fix. I did take the other back and put it back in.

Go over the paper work that came with the tstat. See if you set it all as need be for a heatpump on heat.