Can't connect to inet from one wireless router to another

Can you give the output of:

sudo lshw -C network; lsb_release -a; uname -a; sudo rfkill list

Thanks

[#output 1-16-12 12:09 pm] Thank you, andrew. This morning I got online with this pc (the Dell Dim4500, with the problem) by temporarily moving the Clearwire modem to this location and I wired via ethernet cable it to the Dell pc.
I went online and updated the Ubuntu system. So this output you wanted to see (below) is with me being online right now on the Dell Dim 4500 pc.
Later today I will reinstall the modem back in the living room, hooked up to the Belkin router and the non-problematic pc. Then I will reconnect the Netgear router back here in the dining room's Dell computer. I will re-command your suggestion again and repost it's resulting output.
cheers ;o)---Leo

leo@leo-DIM4500:~$ sudo lshw -C network; lsb_release -a; uname -a; sudo rfkill list
[sudo] password for leo:
  *-network
       description: Ethernet interface
       product: 21x4x DEC-Tulip compatible 10/100 Ethernet
       vendor: Davicom Semiconductor, Inc.
       physical id: 0
       bus info: pci@0000:02:00.0
       logical name: eth0
       version: 31
       serial: 00:08:a1:22:33:e7
       width: 32 bits
       clock: 33MHz
       capabilities: pm bus_master cap_list rom ethernet physical
       configuration: broadcast=yes driver=dmfe driverversion=1.36.4 ip=192.168.15.2 latency=64 link=yes maxlatency=40 mingnt=20 multicast=yes
       resources: irq:21 ioport:d800(size=256) memory:feaffc00-feaffcff memory:fea80000-feabffff
No LSB modules are available.
Distributor ID: Ubuntu
Description: Ubuntu 11.10
Release: 11.10
Codename: oneiric
Linux leo-DIM4500 3.0.0-14-generic #23-Ubuntu SMP Mon Nov 21 20:34:47 UTC 2011 i686 i686 i386 GNU/Linux
sudo: rfkill: command not found
leo@leo-DIM4500:~$

Ok, I'm back...I now back to the original setup: Here in the living room with Pent III computer, Clearwire modem, and Belkin wireless router.
The "problem pc", in the dining room, successfully connected to the Netgear wireless router via ethernet cable, and I can connect to the Netgear setup program via my browser (http://www.loginrouter.net) ). I still can't connect to this Belkin Router via wireless.
I typed in the (above) sudo commands on the problem pc, and the output is the same as earlier this morning (above).
I tried several different methods, to connect the routers w/each other, per instructions on the Netgear page, e.g., pin method, automatically search and find connections, manually configure, etc. By the way, the manual method is a bit awkward for me, as I get confused which MAC address to use, which router is the host or client, etc.
Might it be possible that I'd be better off getting a usb or PCI card type wireless device, and dump the idea of trying to get these 2 routers to interconnect?

p.s. Do you know of a good link that explains the details of using the Network Connections program inb Ubuntu, and explanations of it's various windows, terminology, etc.?

I've been searching lots of forums looking for answers to my dilemna. Quite frankly I can't recall which Q&A forum this morning got me thinking.....it seems 2 wireless routers can work against each other, especially if they are on the same channel.
That thought stuck in my mind, so I decided to go to my local Best Buy Store, which has gobs of computer related items, TVs, etc. I purchased a Belkin N300 Wireless USB Adapter, plugged it in, and it basically installed itself and I automatically discovered about a dozen wireless sites in my neighborhood, including my running Belkin router in the adjacent living room. I clicked it...and VOILA!!!! I was online within a minute of plugging it into my pc's USB front port.
;o)))))) I am a happy camper.
Thank you all so very much for all your support. I am learning a lot of stuff from y'all in a relatively short length of time.
~Leo