Truck runs rough

If one of the coil packs is bad, it will create a misfire. That would set the check engine light (actually flashing when missing). When you scan the computer, you will have P03XX codes. Each code will indicate a different cylinder with the misfire. For example, P0301 would indicate cylinder. A P0305 would indicate cylinder five misfire. That is how you can determine which cylinder is missing (if that is the case). Often times, when you get that many miles, the catalytic converter will begin to plug causing excessive back pressure and a loss of power. If the check engine light is on, have the computer scanned to determine what codes are present. Once you do that, let me know if you have a code you do not understand, and I can try to help you through it.

There is no check engine light yet. But it was when I first got the vehicle it went off when I disconnected the battery to change the starter. So what do I check next, the catalytic converter? And not that, then what, a sensor?

To me it sounds like you may have lost compression in one or more cylinders. Here are some guides to help us get started.

https://www.2carpros.com/articles/how-to-test-engine-compression

and

https://www.2carpros.com/articles/engine-misfires-or-runs-rough

Please let us know what you find. We are interested to see what it is.

Cheers, Ken