Mapping a com port our network

You can certainly share the printer as a network printer and I think what you are saying is that the server has an internet connection and you want to share that with other computers?

For the Printer, just select "Start", Settings, Printers. Install a printer then left click over the printer Icon and select sharing. At the printer property page change the radio button from "Not Shared to "Shared as" and give it a share name.

For the com port left click over "My Network Places" on your desktop then choose "Properties". Select the connection you want to share and select "Properties" then select the Sharing Tab. Select the Internet connection sharing option. Be careful the IP address assigned to the NIC might get change if it is static.You just need to reset it back.

If my guess is wrong and you really want to share the computers com port then the answer is no. You can redirect LPT to a com port and use a serial printer but I haven't seen that done for years.