I'm on dial-up as well, so no problem there, I have mine to check and notify me "Ask when update is available" rather than "manual" which would disable the automatic update.
I also note that you state that you have version 4.5, the latest version is 4.6.691 so if that is correct then it has been a considerable time since you updated.
Try a repair of avast. Add Remove programs, avast! Anti-Virus, Change/Remove button and scroll down to Repair, click next and follow. You need to be on-line to do this.
If that doesn't work try, uninstall, reboot, install, reboot. However, since your program would appear to be well out of date, it may be advisable to download avast again, uninstall the current version, boot and install the latest version.
If you haven't kept a copy of the registration key you can register again and get a new one.