Thanks to this thread the matter is now solved
If indeed there were a T-Mobile outage [which means lack of service by T-Mo] in the beginning, the scarcity of similar experiences by people in a metropolitan area as big as LA means it must have been over soon.
Conclusion: the fault lay not in my stars but in my Blackberry.
I pulled the battery, polished and reseated the SIM card, and that was it. Fixed!
In effect though, you, the participants in the thread, fixed my BlackBerry.
Thank you!