Sounds like you have a bad ground / negative battery cable connection to the frame. The very first thing I'd do is unhook battery, remove battery tray (4 bolts, 10mm) and then remove the ground wire that goes from the negative battery cable to the fender well just under the battery tray. Grind the paint off of the area around the bolt with some coarse sandpaper, sand the washer end of the negative battery cable that attaches to the fender, and the bolt threads that attach it all together, and then wipe it clean with acetone. Now apply dielectric grease to all the areas you sanded, and reassemble it all. This is vital to do on old / high mileage vehicles. Bad grounds can cause fires, blown fuses and relays and sensor / instrument failures. Battery wont be charged by the alternator if it doesn't have a good ground connection. Alternator swap in a shop is $500 and wont fix the problem. A new battery is $75 and wont fix the problem (for very long) and will kill the new battery eventually too. Start with the ground cable or just run a new ground wire altogether from negative battery post to the frame somewhere (remove paint and use electric grease to prevent future corrosion!). Then go from there. Let me know after you do that if you still have problems.