Is it the 2.2 Litre engine. Or the 3.4L?
The transmissions they used on those aren't typically known for having a lot of problems. Ofcourse there is always going to be one bad seed, but for the most part they are okay. Are you going to diagnostic shops, or Transmission shops? Your average technician doesn't really know how to diagnose a transmission issue. I've been doing diagnostics for 10 years, and still really don't know as much the transmission shop guys do.
This however sounds like, you're having an issue with one the shifting solenoids inside the transmission. They're basically little actuators that block and allow flow of transmission fluid through channels that enable the gears to shift or move. If these channels, the oil pan, or actuators are compromised it will inhibit the transmission's ability to shift.
Unfortunately GM has limited transmission support for OBD. You could have the dealership use their in house scan tool to run diagnostics on it. If that fails, you may need to replace the transmission. It's essentially idiopathic at that point unless you remove the transmission and disassemble it to find the reason it malfunctioned.