If 3rd clutches or sprag are bad it will act like this and will seem stuck in 2nd until the 3-4 shift.
Under light throttle it will shift 1-2 around 13 mph, 2-3 shift about 25 mph, and 3-4 shift at 44 mph. This is based off of a 99 file and will vary a bit depending on throttle position but is your average shift speed ranges.
With your SnapOn Modis you just need to get into the Transmission data menu and watch "Gear" or "Current Gear" and it will show 1-2-3-4 based on what the pcm commands. Odds are around 25mph you will see 3rd gear commanded but no rpm change. You can also watch "Gear Ratio" and it should read 1.00 in 3rd gear. If it is still showing around 1.6 ratio after the 3rd is commanded that is saying the computer is doing its job. Since you have 1st, 2nd, and 4th that is proving both shift solenoids work.
Another crude test you can do is unplug the main transmission case connector under the throttle body area. It is a round 20 way connector. Squeeze the sides and pull it back. There is no electrical control at this point and gives limited operation. You will have max line pressure, Reverse, 3rd gear in D and 3 ranges, and 2nd gear in 2 and 1 ranges. You may have 3rd when doing this due to the max line pressure but if you take off in 1st or 2nd range (will be in 2nd) and upshift to 3rd and still no change then it is definitely internal and proves a 3rd clutch or sprag problem. Not uncommon on the 97-02 models, sorry I didn't see mention of the year of your car. Hope this helps
