Interior light quit working

You're bouncing all over the place. First of all, the radio quit because the memory circuit is tied in with the interior lights. Fix the light problem and replace the blown fuse.

You need to be WAY more specific about the no-start condition. "Doesn't start" is equivalent to saying, "I'm in pain". Does it crank normally? Does it crank too slowly? What happens to the brightness of the headlights when you try to crank it? Have you checked for spark, fuel pressure, diagnostic fault codes?

Sorry for the delay in responding.

Lets back up a minute. The alternator recharges the battery when the engine is running. To say it's not charging would imply the engine was running when it was being tested. To say it's discharging could mean exactly the same thing or it could mean anything that is working, like lights and horn, is discharging the battery. Can I guess the engine started and ran once the new battery was installed? If that is right, can you put your hands on an inexpensive digital voltmeter? Harbor Freight Tools has them on sale all the time for 5 bucks or less.

We need the engine running to do the tests, and you will need to take 6 voltage readings; four with the engine running, and two with it off. Those readings with the engine running are: 1) right across the battery, 2) the large output wire bolted to the back of the alternator, 3, 4) the two smaller wires bolted to the back of the alternator. There will be a small black plastic block on the back with all three wires going into it, and two tiny nuts on tabs for those two small wires. You must measure right on those two little nuts, but if they're rusty, (like normal), you'll have to scratch them with the meter probes to get a good reading.

With the engine off just remeasure the battery voltage and the voltage on the large output wire bolted on the back of the alternator.

Not sure how to interpret "goes dead" but it reminds me of another concern. If you mean the engine stalls right after starting it, that is most likely due to replacing the battery. The Engine Computer lost its memory and has to relearn "minimum throttle" before it will know when it has to be in control of idle speed. Until that occurs, you won't get the nice "idle flare-up" to 1500 rpm when you start the engine and you will have to hold the gas pedal down 1/8" to keep the engine running.

If that sounds like I described it right, go out and drive it. Once you hit highway speed with the engine warmed up, coast for at least seven seconds without touching the pedals. That will meet the conditions needed for the relearn to take place.

If by "going dead" you mean electrical stuff goes off, that's a different problem.