After a power failure I had to disconnect the phone connection to my Esprit 738 Express alarm system because it makes a buzzing sound and the phone line goes dead, the phones start working again a minute or so after the alarm is disconnected.

Can I reset the panel or did it get fried...

Does your system have a little square box, probably tan colored, with a wire going in one side and another with a phone-type plug on one end and some wires going to your panel on the other? That's called an RJ31X, and it could be your problem.

Try plugging a phone directly into the 31x. If your other phones go dead, the 31x is the problem. If you plug your system into it and the phones go dead, the panel is the problem.

I disconnected the cord that plugs into the RJ31x ,hooked a regular phone to it and once again had that buzzing sound ,so I guess that's the part that fried. I will replace that part and see what happens, thank's for your help !

You may have a grounded protector, or one of the phone lines touching ground.
Disconnect at "D Marc"(outside box) if hum goes away, problem is in house, if not, it is Telco Problem.

Good point, Strat. I neglected to mention that.