I tried it now, I could not type in my hyperterminal anymore as soon as I connected my modem to the PC with only 3 wires. As soon as I connected 9 pin serial cable, everything starts working fine.
Was hyperterminal in hand shaking mode?

See the modem manual, if the modem is in handshaking mode by default, in such a case you have to set it for no flux controll.

Al.