What type of network should I set up?

I live in a college where I have no administrative access to the wireless router that is set up in my hall. In my own room I have a desktop (wired only) a laptop and a tablet. I am trying to set up a network within my own room for my three devices. I have two routers, one of which can function as a bridge, repeater, or in station-infrastructure mode. However, after many hours and trying all the options, I do not seem to be able to get the setup working. What I am trying to do is have the router with many options pick up the wireless signal from the college's AP. I want it to pass that on (wired) to a regular router, which will then distribute it to my devices (particularly to my desktop). Any suggestions as to what setting my router should be set up as or if this type of set-up is even possible (attaching a second bridge to the college's AP is impossible because, as a student, I do not have administrative access)?

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Clarification Request
Diagram for clarification
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Keep in mind that

I've set up such with only 2 of those boxes. The recipe is known and something I've done in a pinch dozens of times now. The cool thing about it is the setup time for me is down to about 15 minutes.

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So you need a new recipe?

I don't write tutorials but here's a recipe.

1. Install Virtual Router on a Windows 7 laptop.
2. Google "How to use a router as a WAP" and plug an Ethernet cable to one of the LAN ports of that router and your laptop.

Something I've done in about 15 minutes.

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Prefer not to use laptop in order to give desktop Internet

Though this would be a solution (or, an analogous one - I run Ubuntu 12.04 as my OS and so I could set up a VLAN through that) it would require my laptop to be on in order for my desktop to have Internet access. It would also require twice as many packets to be sent: one to the wireless AP, one from the Laptop to the "college router" and then two in the reverse direction. Available space as well as the fact that the laptop is brought to classes would make this solution less than optimal in my situation.

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Good luck.

Sorry but if your recipe was going to work then it would be done and done. As Virtual Router could be run on the desktop then why not do that? WiFi for the desktop would be under 8 bucks.

I'm unsure why folk work so hard when there are working solutions or recipes. Usually you have to let them flop around a while.

-> OK here's an idea. Why not ask your college IT how to do this? If anyone would know, they would.

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PS. The cheapie I carry to add WiFi cheaply.

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