I started getting this before my tranny went AWOL. I found, if I floored the throttle, it would then change up. I wouldn't take it to the redline though
After a few seconds, it would then quit 3rd or 4th gear, and go back to 2nd again. and i'd have to do the same again to get it to change up. The cause was water in the transmission fluid (from the tranny's radiator), the cost was rather high.