Modem works on 1 computer, not the other

[Poda]

I can't figure this out. I have an external USR 56k modem. I hook it up via the serial port on COM1 to Computer 1. The modem will dial out and pick up. I hook it up via the serial port on COM1 to Computer 2. The modem will dial out, but it won't pick up. So, summary

Computer 1 and Computer 2 both have 2 serial ports enabled to COM1 and COM2 in the BIOS.
Computer 1 and Computer 2 both have the same OS (Windows 98).
Computer 1 and Computer 2 both have the exact same "looking" serial ports, 9 pins on the back.

So, my thought is there is some type of difference between the serial ports on Computer 1 and the serial ports on Computer 2.

Computer 1 has a Matsonic MS6260S motherboard.
Computer 2 has an ECS K7S5A motherboard.

Any help would be appreciated. Thanks.

 

[Poda]

Now, I'm getting strange results on both. I can't dial out of Phone Dialer or HyperTerminal. I get a No Dialtone error.