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Starting problems are actually pretty easy to diagnose. With a fully charged battery, the engine should crank over. If it doesn't, try shorting the terminals on the starter relay on the passenger's fenderwell. If it cranks over and starts, then it's either the starter relay itself or the ignition switch in the column. If it still won't crank or cranks but sounds weak and won't start, it's either the battery cables themselves or the starter.
Charging problems are different, and are usually either a worn out alternator or dying battery. Best bet there is to take both to a parts store and have them tested.
Had a similar problem with my 95 f150! had new battery,starter,alt ended up being the starter not being grounded out. there was oil between the starter and bellhouseing cleaned it and ran a ground from the starter to frame took care of the problem.hope this helps also had same problem with 88 f250
If that doesn't work check your ground cable from firewall to engine block (or bracket attached to block). If it is loose, it will not start. If you can jump the solenoid though, that's where I'd start with parts. Checking cables and cleaning connections is still free.