Basically, since the 3-4 upshift is controlled by the computer, any one of the five things listed would (rightly) keep the computer from letting you upshift into 4th gear (OD).
1) Let's take the throttle position sensor for example - if you are standing on the gas, the computer thinks you are trying to get past somebody (it might even downshift for a pass, depending on how hard you are stepping on the gas). In that case, it will keep you in third gear until you are past that person and let up on the gas (closing the throttle).
2) Vehicle speed sensor - if you aren't going fast enough, the computer realizes that shifting into a higher gear will lower the engine RPMs below the "powerband" of the engine (potentially stalling the motor if it can't keep turning with enough power), so it won't give the command to upshift into 4th gear.
3) Coolant temperature switch - if the coolant temperature is too high/too low, it won't allow the shift for "self-preservation" reasons. It want's you to go easy and get off the highway.
4) Brake light switch - if you are on the brakes, you are trying to slow down, so you obviously don't need to get into a higher gear.
5) MAP sensor - this stands for Manifold Air Pressure sensor. It is another way of seeing if you are standing on the gas pedal (throttle) trying to pass somebody.
The 3-4 shift is controlled by the computer (by means of a solenoid valve), so if the computer thinks you shouldn't shift into 4th gear, it won't do it. The five things I went over above are how it decides on if you should shift or not. These things are "input" into the computer by means of sensors. If these sensors are giving bad information, the computer doesn't necessarily know (like having bad advisors or a blind seeing-eye dog).
I was trying to say that the computer would be the last thing I would suspect, but it is possible. I'm not sure of how to keep you from getting ripped off. If you ask for the original computer module back, there is no guarantee that he won't get one from a junkyard and present it to you as proof. I'm just not a super-trusting kind of person. These links give ways of testing the solenoid and transmission (output) so that it can be narrowed down to the computer or what the computer relies on to make it's decisions. If all five things on the "input" side of the computer can be eliminated, and the "output" side is still not right, then I guess it has to be the computer.
If you search eBay for Explorer CPU, they have some later year ones for less than $50. I'd be very surprised if the earlier ones couldn't be had even cheaper.