|Somebody really wasn't thinking when they terminated the cables in a closet with no electrical plugs. However, I'm betting there's an electrical outlet within 10 feet (say 3 m) of the closet, likely more like 6' or 2m|
Why not put a little shelf in the closet just under the patch panel (where the network cables terminate) and run an extension cord from the nearest power outlet to the shelf and then plug your router/modem in there?
You didn't mention where your nearest phone line is. If there's one in the same room, you could run it from the wall outlet to the closet to the ADSL modem.
Using 2 routers one stays in the main bedroom and one in the other bedroom where I also need faster internet (wireless too slow).
Using a switch (I have no idea how to hook it up)
I'm guessing by this you mean you need more than one network connection in this room, but only have one coming out of the wall. If this is correct, then a switch would be the best way to go. These days a switch is pretty easy to connect. Simply plug one of the ports on the switch into the wall outlet. At the other end, plug it into a LAN port on the router. No configuration required.
Keep in mind, if you have a SOHO router with 4 LAN ports and you need more connections, you'll need a switch setup in that closet too.
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.