1996 Ford E-Series Van fan starts 3 out o4 4 times or less

I replaced the somewhat corroded battery terminals when it started to need jumping off. I thought it was fixed, but now it will stzrt sometimes, then not start l minute later. Turns over, not making a bad starter noise, starts immediately when jumped off. 2 places checked battery and alternator and said they were fine. The battery is old. I'm sure the alternator is, too; new water pump, thermostat, fan shroud, needs a tuneup! The van was in the nickel and dime stage when I bought it, but I am happy with it, paid not very much. I am diisabled, with no income, a friend helps me, trying to get parts from auto salvage but don't have money to try every possibility. I've heard it might be the ignition switch, I know the linkage is slipping, I have to hold the gear shift up to stzrt sometimes; the linkage has been getting a little worse for year

Thank you so much for any suggestions you can give me.