Adding to most of the replies already made.
If you are accessing the router via a WIRELESS connection check that it's at least operating at "modern" type speeds -- if it's really old it *could* be worth replacing.
Your pre 2000 router will certainly be the older 801-b (max 11 mbs and unsuitable for faster internet connections such as current 20mbs and faster service providers). It probably also will have a max 1GB LAN connection. Modern Routers will give up to 1000 GB via a Lan (although I haven't yet seen any ISP's offering anywhere near that speed -- however on a Network the 1000 GB speed is great).
Wireless cards in modern laptops won't be a problem -- nor will the LAN card if you are connecting to the router via a LAN cable.
Have a read of this first before replacing the router. IMO it's probably worth replacing and these aren't expensive either. Wireless router buying guide - Wireless router reviews - Computing - Which? Technology
Check also what Internet Speed you are getting -- In the UK if it's B.T you could be getting speeds as low as 0.5 Mb/s -- even mobile phone broadband is much faster than that --
BT have been known to CAP accounts drastically without telling the account holder -- on my last trip to the UK while helping a colleague with slow Internet I had to spend HOURS on the phone with a really Horrible remote call centre where the operator just refused point blank to check the speed saying the account was Paying for 20 mbs --she couldn't understand the user was only getting 0.5 mbs.
Any router will show the connection speed --and there are enough tests on the net too if you can't login to your routers control panel. Speedtest.net - The Global Broadband Speed Test
(BTW my colleague changed to SKY Broadband after our experience with BT and has been totally satisfied ever since. The woman in the Call center was obviously reading from a prepared script and was totally incapable of actually checking what speed the account was physically getting -- a 5 second test as above would have shown !!!!).