98 Ford Explorer won't shift into overdrive

Got a call from my little sister about two weeks ago that her Ford Explorer would not drive forward. Checked it out and put it into second to get it home.
Last weekend me and my dad changed the filter and fluid and then drove it for a bit.
It sounded a little better but still would go into drive or reverse. We shifted into second which we knew worked and then back into reverse immediately and now reverse worked, although sluggish. The same was true for drive.
A few days later dad changed a solenoid and now it will go into drive and go up to 15mph, but will not shift from first to overdrive first. And still no reverse right away.
She is able to get to school with second gear and pop into drive when she gets up to 40-45mph. If she has to backup from start, first she has to put it into second and then back to reverse.
Something in overdrive doesn’t seem to be doing its job right. Any ideas from the shadetree community would be welcome as to where to go from here.
She is looking to replace the truck in the near future for a used car with better gas mileage when she gets some money saved. Just trying to buy her some time. Thanks for any help.

This is probably going to require a good transmission shop’s help. But if you feel lucky you could try a proper transmission service. Might help. Remove & drain the pan, clean the bottom of the pan, inspecting for metal debris, and replace the transmission filter. Refill.

BTW, when you say it won’t shift from first to overdrive, that isn’t something it will normally do even when it works correctly, right?

Just my two cents and not really worth that. They already changed the filter and dropped the pan. Sometimes the default for problem transmission will be 2nd gear. It does that so you can at least get home. The only time that happened to me, it was a set of solenoids that solved the problem, not just one, but that was GM not Ford. So I think their are either more solenoids that need attention, an electronic problem, or a major trans problem. I think a shop needs to take a look at it, so it might be just stepping up replacement a little sooner. These things never happen at convenient times.

Try also to pull codes to check if there’s any failure that causes the pcm to wrongly decide not to shift. Mechanical problem within the transmission is difficult to trace.