1986 Honda CRX carb issues

I bought this 1986 Honda CRX, automatic, carburated and it was popping the alternator/carburator solenoid fuse every time the key was turned on. The short was in the thermostat located under the distributor. I disconected the black/yellow wire going to the thermostat (has positive juice to it) and now I am not popping fuses. I can get it to start by pouring a little gas in the carb and then it idles fine or I can rev it up for a while, but after about 45 seconds, something is cutting the fuel and it dies. I have good fuel flow to the carb (it has a mechanical fuel pump located on top of the motor). All the vacume lines seem to be hooked up. I even tried conecting the two wires the go into the thermostat together in an effort to bypass the thermostat and nothing seems to let it keep running. I had the alternator checked when I was popping fuses and it is good. I have been reading about devacing the carb and also about putting a Weber carb on, but I would like to keep it stock if possible. Any help would be greatly appriciated. I am going to give this car to my daughter as a Christmas gift so I have some time to figure it out. Thanks to anyone that can help.