The forum is awful slow today, this is my 4th attempt posting this...
2005s came with either 3.42s or 4.10s and the 17" wheels are most popular, which means you probably have 31.6" tall tires.
By my calculations, 3500rpm with 3.42s corresponds almost exactly with 2nd gear at 60mph. 3rd and 4th gear aren't working. Other usual tire size and gear combinations don't correspond in this manner.
Right up front we can rule out one of the shift solenoids since you have 1st and 2nd gears (both are ON for 1st, only B is on for 2nd, both go OFF for 3rd, while only A is on for 4th gear). Since you have 1st and 2nd, A should be good. The PCM only commands shifts in the 4L60E by turning on/off the two shift solenoids, the shifts are still accomplished hydraulically.
If solenoid B is stuck/jammed on then it can't shift to 3rd or 4th gear since oil will not be directed to the 3rd circuit (which runs partially through the 2nd circuit as oil is passed to the back side of the 2nd gear servo). A and B are both on in park, neutral, and reverse, so this seems reasonable.
First go to autozone and get them to check for error codes, if there are any post the number code here. Replacing shift solenoid B may fix the problem since it should simply be OFF for 3rd and 4th gear and ON any other time.
I have some more ideas if this doesn't work. Simply trying to eliminate the easiest/cheapest options first.
Before confusing anyone, a no 2-3 shift condition is much different than a no 3rd gear condition. As long as it is stuck in 2nd gear the problem is probably minor. If it freewheels (rpm climbs rapidly to 4k+) on what's supposed to be a shift into 3rd or (sometimes) 4th, then the direct clutch is dead and a rebuild will be needed.
