Talk about coincidence. My remote for this same alarm (350HV) started giving problems a few weeks ago. It just wouldn't work intermittently - had to press the arm/disarm button down longer and harder for it to work. Just thought the battery was dying.
Then last Thursday it stopped working altogether. I opened it up thinking the battery died and swapped it with the spare remote battery (that remote is working perfectly) but had the same problem.
Turned out that the silver battery holder/connector separated from the circuit board. Just had to solder it back on and it's working fine now with the old battery.
This may not be your problem though. I knew power/battery was my problem because when my remote was giving problems, if I pressed the arm/disarm button the light on the remote wasn't flashing. If yours flashes when you press the button (meaning it's getting power) and it still doesn't disarm the car, then you may have a more serious problem like your alarm tech suggested.
But before I shell out $400, I'd google the topic to see if it's something I could fix myself. Just a couple quick links I found with a search for "Viper remote problems":
http://forum.ecoustics.com/bbs/messages/4/118785.html
http://www.tech78.com/auto/viper-550-remote_43815.html
http://www.gtaforums.com/index.php?showtopic=298101
These may not solve your problem, but just keep googling and you may find a solution.
