The 4L80E uses a low/reverse band. Even if the computer fails completely the transmission locks into second gear, boosts the line pressure, and reverse would still work. It could be the band, band servo, or overrun sprag. To test if its a band issue, run it up till it shifts into third, but not too fast (40-ish) and then manually downshift to low. If the truck doesn't downshift, the band isn't applying. I worked on these installed in up-armored Humvees, and we did occasionally break bands and band retaining pins from beating on them with the big tires and porky weight of those vehicles.
This is a fairly common complaint, if all the forward gears work fine, and the fluid level is good, I'd check the servo/servo seal first, as they are sensitive to band wear and may require adjustment, as this is the cheapest and easiest to fix. Bands/overruns mean a rebuild.
Since its an electronic transmission, you may want to read the trouble codes (if any) which might help narrow down an issue. Hopefully others will chime in. In my experience it has never been good news when this happens.
