I'm wondering exactly what the wireless interface in that laptop is, as a) there might be technologies in that which are somewhat at odds with the router (mainly interraction between 802.11b (which is a possibilty given the age of the laptop) and 802.11b/g/<and later> devices); and b) it might be worth throwing the latest driver at it for starters; and with a bit more knowledge of the kit involved, there are a few more tweaks we could try - changing the radio channel used etc.
So, if you go into Device Manager (right click on 'My Computer' and select properties from the list, then click the Hardware Tab then Device Manager button (Windows XP), or just click Device Manager (Vista/7), you'll get a tree showing all the hardware in the machine... Roughly 2/3 of the way down you should have a section for 'Network Adapters' - in there it should list your wireless adapter - first it'd be useful to know what's listed there; and after than if you double-click it, and choose the 'Details' tab, you should be able to get the Hardware (/Device) IDs (you may have to select that from a drop-down). The string which should start something like PCI\VEN....... would be handy too. Oh, the model number of the D-Link router would be good too mate...
Also, if any of the fiddling we can try doesn't fix it, there's always the option of disabling the on-board wireless and throwing a D-Link wireless dongle at it, which would probably only cost £10-£20. We'll cross that bridge when we come to it though eh...
All the best mate,
Rob.