You say “tried”. Did it actually work? If you had no service out where you were camping, that could explain the problem all by itself. When your phone is searching for service, it uses more battery power than when it has found service and knows exactly how much power it needs to transmit with. A lot of phones will shut off after searching for a certain amount of time, because searching all night runs down your battery.
There’s digital TDMA too. Before AT&T Wireless and Cingular (now the same company) offered GSM, they had digital TDMA. In fact, GSM is a TDMA system - it’s not compatible with the other one, but it divides each frequency into timeslices. I believe Nextel’s iDEN is also a TDMA system.
This is a feature of CDMA, not the frequency band (“PCS” refers to the 1900 MHz band, and “cellular” to the 800 MHz band, not that most people use the terms that way). It’s called “soft handoff”, and I wasn’t aware GSM had anything similar.