Home Forums Networks & Cross-Platform Networking Dial-up access and "theft" via modem

Curious and disturbing related situations:

#1: The other day, when checking my call logins as registered by my ISP, I noticed a number of calls/logins on my account which were not attributable to me (ie, they occurred at times during which my computer and telephone were not in use), generally around the midnight hour and for 40-80 minutes' duration.
The only explanation I can come up with — given that only I have access to my computer and telephone and knowledge of my account number and login password (PW) — is that someone at the ISP was taking advantage of knowing my account number and password (which I "had" to give on some occasion to troubleshoot online access) and was accessing my account for his/her purposes; why, I cannot fathom.
So I contacted the ISP to have the situation investigated (results not back yet) and was advised to change my login PW online so that it could not be viewed/used by anyone other than me (including ISP staff).

EDIT:
I think I've resolved issue #1: For some reason the ISP's call logs seem to be 2 hours out of synch with my time (which would put their server in PST). So issue #1 would seem to be no longer an issue. But issue #2 still is.

#2: I followed through, entering and applying the new PW as appropriate in the Network Preferences panel, waiting over 1.5 hours for the PW to be registered/activated and changing email and other applications requiring the PW. However, after resetting the Network Preferences dial-up information to the new PW, it resulted in authentication failing and access denied. Only the old PW will work to access Internet, but only the new PW functions in accessing my ISP account once online (ie, logged in).
This shouldn't be happening, and yet it is ... or at least seems to be.

Any ideas about what's going on?!

FYI: Access to Internet via USRobotics USB Modem, Model USR5637; regular dial-up (ie, no DSL) service.