Ti800 modem gone bad?

[paulatx1 at aol.com]

Sunday during the Superbowl, my PC-using aunt asked to use my Ti to get online.  She got online, went to a website, and before the website could finish loading...the entire computer froze up!  I have NEVER had this entire computer lock up since switching to Jaguar.  I have had a few apps  freeze,  but never the entire computer.    I restarted the machine by hitting the powerbutton, and everything seemed okay...so she got online again.  Went to a different website...and the same thing happened again!   Restarted by hitting the power button, but, this time, we could not get online.  [Software just hung up during the dialing process, never giving an error message.]   
    I ran the hardware test disc  and all it says is that the modem is detected (but it never says it was being tested  or that it passed).  I booted back down to 9.2.2  and I get a "modem cannot be found" error from AOL software.  I booted back to OSX, created a new user, tried to sign online  and get a "modem cannot be found" error message.  
     I checked the phone lines (used a working line from the iBook  with no change in results.)  I reinstalled AOL software.
     I called AppleCare  and the tech decided after a few minutes that it must be a defective modem and that I should send it in for repair  and that the turnaround time would be minimum 5 to 7 days.  
      Where do you have to live to get a 2 day turn around time?  Or who do you have to be?  
     More importantly,  does anyone else have any other ideas I can check  before turning loose of my computer?  
     [And before somebody tells me to lose AOL,  I've been using AOL, without problems,  since 1988...just as long as I have owned Macs...so it isn't very likely that I'm going to change ISPs now.]  
               Paula...hoping for a software fix