Here's what comes to my mind ...and what I would check if it were my tk. These are all relatively easy and quick to do:
1) Engine mounts: Maybe a bolt vibrated loose, or an engine mount gave way. Raise the hood, put in gear (foot on the brake) and give it some 'gas'. See if the engine tilts or raises. Then put it in Reverse and do the same (also foot on the brake).
2) Sticking Brake Pad: The pads can corrode and become lodged in their sliding bosses. This probably isn't b/c by now it would have worn down a pad (maybe). I would check it just the same. Probably simply removing the wheel and backing off the caliper a little with a screwdriver ...and wiggling the brake pads (also with a screwdriver) ..should do the trick. If they are really stuck, that's probably the problem. If they wiggle freely, then it probably isn't. If the rotors look excessively worn, glazed, or corroded, then you probably need to do the brake and there may be a hidden issue there (like a ridge worn into the knuckle ..where the pad slides).
3) Front Diff: It's possible the bolts to the front diff have loosened (or a bushing) has failed, or the diff is somewhat loose. When you go to accelerate, it rocks a little and goes 'pop'. Might not be it but easy to check. Check the intermediate steering shaft for looseness, excessive wear/play as well.
4) Front CV Joints/Axles: Put the truck in N (block the wheels), raise a front wheel off the ground momentarily, then set it back down (that removes any pre-load). Then lift up/down with some force (by hand) on the outer CV inside the front wheel (if it's 4x4). And wiggle up/down on the front driveshafts vigorously. They should feel tight. A small amount of up/down on the outer wheel cv isn't out of the question. A lot of play means something is amiss. Esp with the center shaft between the inner/outer CV joints. Too much movement would produce a 'pop'.
5) Front Driveshaft: While the truck is in N and the pre-load has been taken off the driveline, get under and vigorously wiggle the front driveshaft. Do the same with the rear since you're there. Inspect for excessive 'play'.
6) Wheel bearing/hub assembly: Raise each wheel and vigorously wiggle back and fourth (hands at 12:00 & 6:00). Wiggle violently ..like you mean it. If you feel ANY freeplay whatsoever youhave a wheel bearing failing. While you're there, wiggle in the 3 & 6 oclock positions for any steering 'play'.
7) Misc: If you don't find anything, take it back to the same dealer and have them dig deeper ....or a different dealer/mechanic.
Good luck. Let us know what you find
