Cluster won't effect the trans, it gets told what speed to show from the pcm.
Lhm would have 2 gears (2nd/3rd) and would be triggered by a fault with a code, if none then it will operate normally.
It sounds like the trans is behaving like it isn't getting any power to it except this would throw every fault code related to the trans and cel would be on (just tested that theory, lots of fault codes).
VSS in these transmissions can't be removed and spun to check, they're a reluctor type with the ring pressed onto the output shaft of the trans, but even without a signal being supplied it would start in 1st (unless a code was thrown and we're back to the lhm theory)
and it'd eventually throw a code, pressure switch output to pcm would tell it it's in gear and rpm would tell it that is should be registering a speed.
How was the trans before this happened, any abnormal signs while driving, slipping, sloppy/delayed shifts?
A tech 2 or good scantool would be best then you could see what feedback was coming from the tran to the pcm (pressure switch info, what gear the selector is in etc etc) and what the pcm was telling the trans (what solenoids should be active blah blah)
The mechanic should be able to hook up a pressure gauge onto the trans and monitor fluid pressure, as there's no engagement of gears unless manually selecting 2nd.
What about reverse?
*edit* I keep coming back to mechanical fault in the trans (maybe faulty pcm for the speedo)... but pcm makes no sense for only engaging in 2nd and acting like neutral in other forward gears.
Maybe try it without the transmission fuse in (fuse box under the bonnet) and see what happens, (cel should light up) but see if it'll move forward when other gears.