Hi Pine,
When you say your modem is setup on COM3 (assigned to /dev/ttyS2) - what tool are you using that gives you that information?
When I first setup my 56k modem to use with Linux, I have a dual boot system and was already using WinXP Pro SP2 with a USR 5686D external modem. That is how I bought my system. At that time, I used a guide off of the Internet to do the Linux ppp setup. I think it was this one:
Linux PPP HOWTO.
I am not sure how to answer you question with regard to /dev/ttyS2 vs /sev/ttyS0.
One problem I see is that you are using an intenal hardware modem, whereas all of the advice I have ever seen especially from my PC system vendor advises an external modem be used with Linux. That could be the problem, i.e. there may not be a compatible kernel driver for your internal modem with the Linux release.
It may be that the only way to get connected to the Internet for Linux will be to get yourself a compatible external modem. These days, I use an USR 5686E external modem.
However, with whatever Linux distro you are using, I would visit the distro website and look for modem information, i.e. compatible internal modems with the distro release or whether they recommend external modems.
I could be wrong about all of this, so, good luck in what you find out.
-- Tom