First off, since Linksys released their first draft 802.11g routers at the very end of 2002, I highly doubt that they were still selling 802.11b equipment in 2008 or 2009. But regardless of when you bought it, that technology (802.11b) is now well over a decade old. I assume you're not still running Windows 98 on a 500MHz single-core Pentium III from 1999 as your primary computer. Likewise, it doesn't make a lot of sense to still be running 802.11b.
The rule of thumb with 802.11 products is that you can get TCP throughput of about 50-60% of your signaling rate. With 802.11b you had 4 possible signaling rates: 1, 2, 5.5, and 11 megabits per second. So in a best-case scenario (a perfectly clear channel, and a client that's within a few meters of the router), you could expect TCP throughput of maybe 6 megabits per second, or less than 1 MebiByte per second.
If your channel had other users/interferers, or if your client wasn't close to the router, then you might fall back to the 1 megabit per second data rate, so a TCP download throughput of perhaps just 500 kilobits per second, or 0.477 MebiBytes per second. At that rate, it might take something like 12 seconds to download a 5.5 MebiByte file, assuming negligible latency.
If it's taking you 7 full minutes to download a 5.5 MebiByte file, that's throughput of less than 14 kilobits per second, which is like mid-1990's modem rates. Something is clearly suboptimal with your setup.
That old Linksys 802.11b router doesn't have an analog dial-up modem in it, does it? You are on broadband, aren't you? What speed of broadband Internet connection are you paying for? What speed do you get when you plug a machine directly into your broadband modem via Ethernet? Have you tried changing the channel on the wireless router to find one that's more clear? Try channels 1, 6, and 11, and stick with the one that gives you the best performance.
If you're paying for more than 1.5 megabit per second DSL, then you should definitely upgrade your Wi-Fi beyond 802.11b. Since late 2009, the latest thing is simultaneous dual-band 802.11n with 3 spacial streams, yielding signaling rates up to 450 megabits per second in each band. You can buy an Apple AirPort Extreme wireless router that does that for US$179 MSRP. If that's too expensive, I recommend that you still buy decent simultaneous dual-band 802.11n equipment, but look for something that does 300 megabits per second in 5GHz, and 130-300 megabits per second in 2.4GHz. Don't forget to budget for updated wireless adaptors in your client machines as well. You don't want any old 802.11b equipment around taking up precious airtime if you can avoid it.