A Sea Of Red

I have a question on wireless routers. I'll explain and try to show some type of "digram" to show what I mean because I don't think i'm going to show it properly.

Current setup:
Modem ----> a cable connected to wired router ---> wired router ----> ethernet cable going from wired router to computer ---> computer connected to internet via wires

Could I do this?

Modem ----> a cable connected to wired router ---> wired router ----> ethernet cable going from wired router to wireless router ---> computer connected to wireless internet.

So can I basically plug one ethernet cable to two routers and get access to the internet or does the wireless router have to be directly plugged in to the modem?? Yes I know, why not just ditch the first router and replace it with a wireless router? Problem is that the modem is downstairs because that's where the cable connection is (why? I have no idea...) and we tried replacing the router in the past with a wireless one and the wireless signal is horrible upstairs.

My set up is

Modem ----> a cable connected to wireless router (which has a slot for a WIRED conncetion) ---> wired connection to computer. I have a Linksys router and it covers the whole house...upstairs and down.

yes but that doesn't solve my problem because the wireless signal sucks upstairs, i'm lucky if I get one bar, and that was with a linksys wireless router...

ok, thought of another possible solution:

modem ---> cable to router ----> router ---> ethernet cable to a wireless access point device ---> computer connected to wireless internet

would that work as well??

You don't want to introduce a second router into your setup, because you'll end up with duplicate firewalls and duplicate sets of IP addresses on your LAN. Instead of a wireless router, you need to look for a wireless access point (WAP). Most manufacturers offer their wireless routers just as WAP's without the extra functionality. The connections would look something like this...

Modem -> Router -> Ethernet to WAP -> Wireless clients

You'd still have LAN Ethernet ports free on the router for other wired clients near the router, or you could provide wireless to any clients in range of your signal.

i used to have a very bad signal in my room and in the den. I purchased a D-link antenna from Best Buy to increase the signal. That antenna would replace the original antenna that came with the router and the signal is good all over the house.

Thanks Scorcho, my dad finally answered the phone and he said I could do what I want to do, rather it be router or access point. To me the access point seems to make more sense after doing some brief research on them. Changing the router can be a pain in the butt, I had to replace the first one I had and for some reason it was just a pain trying to get it to work right, so with the access point I won't end up changing any firewall or IP stuff so hopefully I can just plug it in and that's it. Another reason I want to do this is because i'm looking at getting a PDA or an iPod Touch with wifi. Leaning toward the Touch because you can now install apps on it, and apparently it's significantly easier to install apps on the Touch wirelessly than any other way, plus I'd like to be able to lay in bed and be on the internet and connect my DS wirelessly (apparently nintendo is going to be starting a service where you can download games and/or demos, which would be nice to be able to do).