My old modem died resently (Motorola SB5100) and I got a new one (Motorola SB5101). Also I got a new Router (Netgear Wireless-G Router WGR614). When I have the Ethernet Cable connected directly to the Modem, the internet is fine. But when it is connected through the router, it is slow as heck. I have returned the router and got another of the same model and it still doesn't work. I have tried power-cycling, it works for 5 minutes (I've timed it!) then gets slow again. If it helps, I am using a Vista PC to set it up.
Cordless phones, Microwaves, other wireless networks, Power lines, etc can all slow wireless to a crawl. Also distance and metal between you and the base station. Old houses with plaster lathe walls are the death of wireless.
In an apartment you may also be getting interference from neighbors devices. I had a problem every time I heard a neighbors phone ring.
Log into your router and experiment with changing the channel. You may have to try several times to get one that works.
You can do this by typing 192.168.1.1 into the browser if you have a Netgear. The number is different for other brands.
If that fails try a 5Mhz router or a dual band router that can operate in both 5 and 2.4 Ghz range.