Also, the Serial I/O is working fine (I checked a chat software using Hyper Terminal)
Once more
succesful testing does not prove the absence of bugs, it proves the absence of known bugs
I am getting VERY tired of hearing "it worked, so it must be right".
How do you know that while your PC will accept the error resulting from the "uC rather than UART crystal", your modem will accept that error as well?

Well sice you "saved" the right crystal did you "save" the MAX232 as well (it is not in yur description). I know that doing without the MAX232 is another thing that "works" if a happenstance succes is considered proof.

Erik