I reinstalled Windows and now my sound doesn't work - how do I fix it?

It's all about the drivers.

Drivers are the software that "know" how particular hardware operates, and interfaces between Windows and that hardware. Drivers translate the generic instructions that Windows gives it (turn up the volume) into instructions that are specific to that hardware ("send value 234 to I/O port 78, now send value 235, now send value 236, ...").

And I do mean "specific to that hardware" quite literally. One sound card's hardware might be controlled in a completely different way than another's. Rather than have Windows have to know about every possible sound card ever made and could possibly be made, drivers are provided for each that perform that translation.

If you don't have the software driver that goes along with a particular piece of hardware then that hardware might as well not exist. In fact, that's exactly what Windows deals with it: without the drivers Windows has no way to control the hardware so it treats it as if it's not there.

Drivers come from two places: your Windows installation, and your hardware manufacturer.

The reason I said that not all Windows installation CDs are the same is that not all have the same mix of drivers. The Vista installation that you began with clearly had the drivers for your sound card. While they may, or may not, have also been included on the Vista installation media you hopefully got when you purchased the machine, the fact is that they were pre-installed, as we might expect on a new machine.

I have no idea where you got your Windows XP installation media, but it's fairly clear that it doesn't have the drivers you need. This is one of the very common differences between installation media provided by different OEMs like HP, Dell or others, and one way that they differ from the retail versions of Windows you might buy in the store. The HP disks may well include additional drivers for HP supported hardware that the Windows disks from other vendors would not include.

I'm guessing that's the issue you're running into here: wherever it came from your Windows XP installation media simply doesn't have the drivers necessary for whatever sound hardware is present on your laptop.

The good news here is that it's typically an easy fix - at least for recent versions of Windows like XP.

In your case, having an HP laptop, I would visit the HP support site. They should have drivers that you can download and install. You'll need to know your laptop's model number, and perhaps some of the options chosen when it was purchased, and the site should guide you to the specific download for the specific audio hardware in your machine.

Download and install that, and your laptops audio should return.

This is true for most major computer vendors like HP, Dell and others. They all take advantage of the internet to have support sites that provide the latest software drivers and updates for the machines that they sell. And most also have fairly active support forums these days where you can get specific help for your computer and hardware from other users and occasionally the vendor's staff as well.

In the case where they don't provide that level of support or you have a custom or "beige-box" machine you might need to actually determine what specific audio hardware is in the computer, and then visit that hardware manufacturer's site for updated drivers. That's not as likely in this case as you're dealing with a laptop, but is very common for custom built machines, or machines from smaller vendors.