You probably fried all the electronics. Take it to a trusted mechanic to diagnose it.
bad battery or bad charger.
That depends upon what the starter problem is. If the battery is exhausted, you can use another vehicle's battery, with jumper cables.
Corroded, loose, or defective battery cables.
Loose cables, bad battery, alternator or starter.
Causes include a weak battery, loose cables, failed starter.
Dead battery? Loose or dirty battery cables? Bad starter solenoid? Bad starter? Neutral switch?
Check fuses.
Check for: 1) dead battery 2) loose or corroded battery cables
You replaced the battery, is it good?? You really haven't given sufficient info. Check the Battery, Cables, Solenoid, Starter. The way I read this is that you put in a new battery and the truck's engine will not turn over when you turn the key. When you jump the truck, it turns over, starts, and runs. Are you jumping from positive to positive and negative to negative on the batteries OR are you going battery post negative on the vehicle giving the jump to a frame, engine bracket, or body metal point on your F150? If you are going positive to positive/negative to negative on the batteries, then I suspect your new battery. If you are hooking the negative jumper up to a ground other than the negative post on your battery, then I would suspect a bad negative cable. Speaking of cables, did you clean any corrosion off of the terminals when you replaced the battery? Corrosion does funny things. If in doubt, replace the battery cables.
Check battery cables for tightness and corrosion also check solenoid trigger wire
Maybe Its Your Battery
Try the cables from your battery and alt. Sometimes these can corrode.