It could be the electric motor that turns your engine over, or 'starter' if you will. It could be bad, also I suggest taking a look at your fuses and relays to make sure nothing is blown. If the electric motor is good, fuses and relays are all in place, have you considered the thought that your engine may be seized? I mean there would be a lot of warning signs prior to engine seizure; smoke, fire, that kind of thing, unless IT DID happen. IF it did, you can turn that engine over as much as you want, those pistons are not going anywhere.
Also, how do you know indefinitely that your battery is good? if your lights work and radio works, that's still not definitive to say your battery is good. If there is not enough charge, your amps are going to read low. Stick a multimeter on it and get a reading.
And how do you KNOW that the battery is "good"? Just because it lights the headlights for a few seconds, and plays the radio doesn't mean it has enough power stored up to turn the starter.
The "one click noise" that you heard COULD be the last attempt of a weak battery to engage the starter before it goes completely dead.
Call someone who actually KNOWS what they are doing, and get it checked out.
Check terminals to make sure you have a good connection. A lot of times that's the problem lol if not then check the wire that goes from the starter solenoid to the battery for loose connection. Or corroded broke wire. If starter is bad hit it with a hammer a couple times (not hard) and it should free up.
I got battery tested... And nothing's wrong with the motor either just randomly didn't work as of a week ago. First problem in a year of owning my truck.
Won't crank battery's good, alternator good, new starter, fuel pump works. Just one click noise upon start. Need help ASAP, dunno what else to do!!!!