Internet is SO slow with Linksys!

Hi, I have an older computer. A Vpr Matrix I'm guessing series 1600 or 1800? I got it in 2002. Anyway, we have Mediacom, and the router used to be Wlan....which ran Okaaaay. I know it's hooked up to computer 1 downstairs, and computer 2 and 3(me) via wireless( really don't know any tech speak, so bear with me.). Ever since Mediacom came by and finally upgraded our router to Linksys, my internet runs soooooooo slow, and often freezes. And of course it'll still say I have an excellent signal. A few times I have lost the signal, but that seems to be typical of Mediacom....another thing that's new is I've had problems several times now with my computer not being able to find a network address. One of my neighbors down the street has wireless internet, and I can sometimes tap in to that. I only receive a very low signal from that, and it still runs WAY faster than my "excellent" signal from Linksys! So I know it's not my computer being slow in general. Grrr! I'm wondering if I need to download something to make it compatible? My computer may be older but it's a good computer! Thanks to anyone who read all that :)