2004 Ford F-250 Not starting

You need more accuracy in those measurements. 12.2 volts indicates a battery is okay but discharged. A fully-charged battery will measure 12.6 volts. First find where the smaller positive battery wire bolts to the under-hood fuse box. Be sure that connection is clean and tight.

Next, measure the battery voltage again while a helper tries to crank the engine. Put the meter probes right on the posts of the battery, not the cable clamps. If the voltage drops a lot, suspect a bad battery. If the voltage stays up near 12.6 volts, move the meter probes to the cable clamps and measure again. If the voltage is lower there, one of those connections still has a problem.

You can do the same test at the fuse box connection. For this one, leave the meter's negative probe on the battery's negative post, but move the positive probe to the stud at the fuse box, not on the terminal that is bolted to it.

An alternate way of doing this test is to put one meter probe on that stud, and the other probe on the terminal. Logic says those two places are the same point, so they should have the same voltage and the meter will read 0 volts, the difference in the two places, but if you DO read a voltage there, that is proof there is not a good physical connection. This test is most accurate when current is trying to flow through the circuit. Turning on the head lights or heater fan will insure that happens, and it will make a bad connection easier to spot.

It's very common to blow fuses when reconnecting a battery, due to current surges from the many computer memory circuits charging up. Check those first.

Can't help with the radio problem. Ford got selfish and followed GM's lead and locked up all their radio service information after 1997. I can still work on a few '98 models but beyond that you're tied to their two grossly-over-priced repair centers through the dealers.

For the ABS issue, start by having the diagnostic fault codes read and recorded. Those will indicate the circuit that needs further diagnosis. If the code refers to a power supply problem, start by making sure the fuse box terminals aren't stretched or corroded. You can usually find a little hole where you can insert a pick to tighten the terminals.

Radios have a memory circuit for the station presets and clock that is always tied to some other circuit that is always live, like interior lights, horn, cigarette lighter, ... Or possibly the memory circuit for the ABS Computer. An intermittent connection on an ABS fuse or somewhere else in that circuit therefore could potentially also affect the radio. Some radios will fine while they're on if a problem occurs in its memory circuit, but most will either go dead, lose sound, or exhibit some other symptom.