[Schnabel]

Wow, that is a real mess you have going there! How about this.
1) Make sure that the very first router (the one by your dad's computer) is the only one assigning ip address's. I don't know how the logitech things work, but I'm guessing that they are just a bridge.
2) Plug the end for your mom's computer into the router by your dad's computer.
3) Bypass the switch in your room and just plug into the wireless router. I assume that the router has wired connections on it.

See if that doesn't help the system out a little. This way if something goes wrong, such as in your room, it doesn't take down your mom's computer.

OR if you don't mind spending some money:
1) Starting with the modem, plug a wireless router into it. Use this as the DHCP Server.
2) Plug your dad's computer into this.
3) Plug one logitech thing into this OR plug in a really long ethernet cable
4) Get a wireless receiver for your mom's computer and plug that into it.
5) Plug the Linksys switch in your room and plug in only the two desktops (use wireless for the laptop)
6) Make sure that the switch in your room has it's DHCP server turned off

OR again if you want to spend the money
1) Move the modem into your room
2) Plug in wireless router
3) Plug in desktops in your room
4) Get wireless receiver for both mom and dad's computer

I'm guessing that, even though they didn't before, your problem is in the logitech wireless things. I think they may be interfering with each other right now, so all of my solutions are aimed at getting you down to 1 or none.

EDIT: Maybe the modem, try logging into it (192.168.0.1 maybe) and see if it has a self check feature. I know mine does, but it is DSL, so you never know. Once you get it working with what ever you plug in, then try what I suggested above. Also, make sure that you plug a router in via the internet port and make the router assign all IP addresses, this way if there is a problem in the network, you can trace it back to one point. I know that sometimes routers will make the modem assign them, and most modems are only able to assign 1.