nimitz
Foxconn made for gateway
The price of a Gateway desktop motherboard can vary widely depending on the model and specifications. Generally, you can expect to pay anywhere from $50 to $150 for a replacement motherboard. For specific pricing, it's best to check online retailers or Gateway's official website for the most current options and availability.
Depending on it's size, it would likely have either an ATX or microATX motherboard.
Host Adapter
mb.wm902.001 This motherboard is also used in some Acer models.
if you do not know where to find the answer for that, buy a computer that is complete already, is my suggestion to you.
plugged into motherboard
Linksys E2000 Advanced Wireless-N Router - CNET Reviews is one place where you can find a comparison of a Belkin router with a Linksys E2000 router and you can make a best decision what to choose.
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Go to the manufacturers website. Or go to the website of the company you bought the computer from (ex. Dell, Gateway, Sony).
You can find some online reviews for the Linksys e2000 router at http://reviews.cnet.com/routers/linksys-e2000-advanced-wireless/4505-3319_7-34103434.html and http://www.pcmag.com/article2/0,2817,2365551,00.asp. It looks like a good router.
The memory will work in the motherboard, but it will downclock to 800 MHz. Purchasing it would thus be a waste, since the motherboard / processor will not be able to utilize it at it's full speed.