Love the picture, by the way
(+1 for that!)
quick question, the switcher
in the picture, is that a phone line filter or a switch for computers?
If it is a filter it needs to be on only the line to a phone, and will interupt your internet.
If it is a switch you should have the hardware in the other order:
2 comps -> switch -> modem -> unblocked phone line.
If you can connect 2 computers by ethernet cables to the modem you modem likely has a small router built in and a switch would not be necessary, unless it adds wireless.
Also the OS is not important when connecting the computers, each computer will individually handle the connection to the modem, router, switch, or what have you if it is setup correctly.