Why is my internet so slow?

Because it's not a big truck.
It's a series of tubes.

And with wifi, there's not even tubes in the series.

Seriously, your problem could be any of the following, and we need more info about your router, about how all the computers connect, about all the computer specs and amount of use, and about what you did when you changed from one laptop to an other with "the same problem."

Lets assume all the computers are on the same wireless connection. If the old and new laptops are 802.11b while the other computers are 802.11g that's a simple explanation. Even if it were reversed, it might explain it, because b has a little more range than g and maybe you're using the old and new laptops a tad far from the router.

Otherwise the old and new laptops could be always in the same location. There could be interference just there. Maybe from another appliance, or some wiring in the wall to that room. Common culprits are: Microwaves, Compressors (in an Air Conditioner or Refrigerator), fans (in anything from an air-filter, to a plasma TV), paper shredders, electric water boilers and in-sink garbage disposals.

It could be the OS or software. You might have replicated the same software to the new machine and been stuck with the same problem. E.G. I've found some virus scanners to run so frequently (daily) for so long (4 hours) while thrashing the disk so much, that general downloading that gets cached to disk or saved is definitely 1/4 regular speed.

Or it could be that all your computers are not treated equally by the router. It might be doing Quality of Service filtering, or it might be lacking proper QoS. In one case it might think that computer is low priority, or in the other case it should be throttling the up-streams of the other machines so that they allow ACK packets through uncontested.

What kind of router? Wireless B routers have had problems with Vista.

Any security suites running? Mcafee/etc can definitely slow down your connection.

Is this a WAN only problem, ie, can you copy files to/from other computers on your LAN without any problems?

If possible I'd try a speed test on both the vista laptop and a non-vista laptop and see how they compare.

Assuming a reasonably powerful computer ram/processor wise Vista shouldn't really be much slower than XP.

Just in case you have a bandwidth-hungry process on your laptop, try NetLimiter or some similar application. It's a sort of task manager for bandwidth usage, and not only will it give you a clearer picture of bandwidth usage, it will also allow you to limit this usage per process.