Hi Lehmag
Disappearing comports !! yep see it a lot in XP (but you failed to state which OS it is), except the other way round that is they show in Device Manager but the com port doesnt work, I usually just remove them under device manager and reboot, however you say they dont show in device manager which is strange, first thing I would do is to reboot the PC and go into the BIOS and see if they are turned on correctly in the BIOS, it may be possible that the system BIOS may have reset to default and the com ports are turned off,
But if the com port is missing then the modem wouldnt find the port and dial out, however you say it seems as though the modem connects, can you verify this at all, ive never used a dial up connection on XP so i'm not sure how you could verify it, im sure someone may have a better idea.
There are a couple of checks you can try
Click Start > run > cmd > enter
type
mode com1 and press enter, it should reply with a list of the port details.
If you get a reply saying invalid port or port not available then there is a problem with the port, or something has opened the port, reboot the PC and as you see the splash screen for XP press F8 and choose safe mode, when logged in try the same command and see what you get.
Its all I can think of for now.
Regards