Installed new battery,now radio and a/c lights cut on and off while driving

Okay. Maybe we went the wrong way here. This could be a voltage regulator or alternator issue. If you don't have the tool(s) it's cheap to purchase an volt/amp meter to see how much power your alternator is releasing. It should be putting well above 12 volts. You do this while the car is running and hook up your tester to the positive battery terminal and a ground. I would also run it under a load (heater, radio, lights and or wipers etc.) Should be in the 13-14 volt range. Some auto parts stores do this test for free, takes about 5 minutes. Your voltage regulator may be starting to fail if it hasn't already. It's a black half moon part attached to the back of your alternator with 2 bolts. If you're not putting out the volts things will act strange and eventually grange the battery. Of course there could be other reasons, but this is where we should have started.

Okay. Maybe we went the wrong way here. This could be a voltage regulator or alternator issue. If you don't have the tool(s) it's cheap to purchase an volt/amp meter to see how much power your alternator is releasing. It should be putting well above 12 volts. You do this while the car is running and hook up your tester to the positive battery terminal and a ground. I would also run it under a load (heater, radio, lights and or wipers etc.) Should be in the 13-14 volt range. Some auto parts stores do this test for free, takes about 5 minutes. Your voltage regulator may be starting to fail if it hasn't already. It's a black half moon part attached to the back of your alternator with 2 bolts. If you're not putting out the volts things will act strange and eventually grange the battery. Of course there could be other reasons, but this is where we should have started.