My Jeep will not stay running after I let off the gas.

Its been giving me problems for a while. All my warning light, gas, seatbelt, oil, engine and airbag, would come on amd my gas gauge and my oil temp gauge would not work. My radio would flash on periodically but never stay on for very long. All while this was going on it continued to drive ok. Then I started it the other day and it took a while to start and when it finally turned over I let off the gas and it died. I did this four times and each time when I let off the gas it dies. I'm thinking possibly alternator what are your thoughts. Thanks