|This isn't really a networking question, it's a phone question.|
However, my department is also responsible for phones so I asked my coworker (we share an office) who has actual training on telephony about this. (I've specialized in networking and have no formal training in telephony).
He frequently connects to our PBX which is several hundred feet away. However, it's not a direct console connection, he has an external modem connected to his PC which in turn plugs into an analog phone line and he dials up the PBX that way.
The software he uses to dialup to the PBX is called "Procomm Plus" but I suspect Hyper Terminal or pretty much any terminal emulation software capable of using a dialup modem to connect.
I would suggest that since you want to connect to a PBX switch, you look at doing it the same way.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.