1991 Geo Metro Battery Drains, Car Stalls and won't start

Something seems to be draining my battery. I took off the alternator and took it to be tested. It tested fine. Thought the old battery had a bad cell, so bought a new one. New one was drained within a week. Symptoms while driving are windshield wipers slow way down, then stop, turn signals slow down then stop, emergency signals and other lights go out. Seems car is trying to run off the battery, then stops when battery is drained. Fully charged new battery, car started OK, but could only drive less than 5 miles before symptoms came up again. Car sputtered, then died while driving. Will not start now. What electrical part would be suspect? Coil? Short. Ignition switch (Tumblers in key ignition are having problems, and hard to get key to work at times.) Car starts fine if I jump start it, but only runs a few minutes. Charging battery while car running does not help. Charging overnight with charger does not help, even on the new battery. Let me know the possible suspects.
Thanks,
Art