Wireless-N router and connection issues?

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For the past several years I have used a Wireless-G router. Gone thru 2 or 3. Few days ago the last one failed and I decided to buy a basic Linksys N router. While using the G routers for the past few years, I rarely if ever had issues with getting disconnected. Since using the N router, I have been getting disconnected it seems at least once an hour. Sometimes more. Also sometimes it says I'm connected but pages do not load. I discovered that I have to be literally next to the router and the issues go away (my "speed" was always 54 Mbps using G routers; now its always 24 Mbps). The issues also seem to go away when I physically connect the cable from the modem directly to the computer, so I dont believe its an ISP problem. Dont know if I am correct, but i am thinking since my computer is 5 years old, therefore maybe not 100% compatible with the router. Is this possible? Are N routers supposed to work flawlessly even with an old computer? Because of that, I am considering going back to using Wireless-G. Please help