@RJNB: Because your internal drive is so small, I disagree with the other posters here. They aren't wrong, but you need more room. And, you want to turn Hibernation OFF. Linux won't work with a hibernated drive. Do you know how to enter BIOS? In HP, you hit the F10 key as soon as you power on. Once you're in the BIOS menu, look for anything about Power Options or putting the computer to sleep. One of these will specify 'Hibernation Enabled', as shown in your Speccy specs. Change it to disabled.
Also, in XP, look at your Power Settings (Control Panel Power Options), Find the 'Hibernate' tab in Power Options Properties, and uncheck 'Hibernate'.
So here's a way to install Linux without even using, your internal hard drive. The instructions below should work with any Linux distro, but I'd suggest you first try Mint17, 32-bit. It comes in various desktop/interface 'flavors'. The KDE flavor (link download locations vary, look toward bottom of that page), is most like XP in its 'intuition', and even has settings designated as Windows so you can make it look 'traditional'.
A smaller version is Linux Mint Mate 32-bit, so maybe try that first, but although it's XP friendly, it's maybe not as full-featured as the KDE. You can see the interface differences once you burn them to DVD.
I say this, because Mint 17 runs well on my Acer A0A 150, which only has 1 GB of RAM, and an Atom processor, which is far weaker than your Pentium M. But Mint is NOT on that computer. I instead installed it to an external drive and to a stick. The drive is 250GB, bigger than my internal drive, so I can download all the programs in Linux if I want. How?
1. Burn each of those download iso's linked, to its own DVD.
2. Turn off your machine, leaving the DVD inside. Wait a few minutes, then turn on machine again.
3. While waiting for the Linux Mint DVD to boot (maybe 10 minutes), go grab some external drive you have or stick, which is at least 32 GB preferably bigger. Pick a drive whose files you don't want, or one that is empty. Or, pick a stick.
4. When it boots, you'll see 'Install Mint' icon almost in the middle of the screen. Hook up that #3 drive/stick to your usb port.
5. Then click on 'Install Mint', and it will present you with both your 37 GB internal drive, and the external. Select the external.
6. At this point, Mint might fight you over the drive being too small. Ignore that, and look for any option to 'free up space' on it, and let it decide the partitioning. You may have to go back and forth to get it to accept the drive (bug in the installer).
7. After it accepts the drive, it will prompt you for a domain/network name. Accept the default.
8. It next prompts you for username and password. DO provide each (have password be as short as possible), and write down what you typed.
9. Go get lunch.
10. In about 30 minutes, you should hear a nice sound telling you the installation is over, with instructions for shutdown. Follow them.
Wash rinse repeat for the other iso.
Now, you're ready to boot in Linux with NO space taken up on your internal hard drive, which is precious. NO changes are made to boot.ini or your mbr, so NO problems with XP. (XP likes to be alone, and on your 37 GB internal hard drive, you want it to be alone.) To boot in XP, just remove the external hard drive or stick, and turn the machine on. It's the same, unchanged XP as it was, prior. 
So to boot in Mint, plug in the external hard drive or stick now containing Mint, and turn on the machine. First time, it takes a good 10 minutes to boot, as it reads what's on your machine, and deploys the right drivers, etc. It's especially compatible with HP, so don't worry about anything.
So now it's booted, you can play. Left click on the menu in left lower corner, just as with XP. Notice all the programs you have. Play with them, see what they do. If you want more, then click on the 'Synaptic Package Manager', type a category. Or, do the same in the Software Manager (which is easier). These 'stores' of programs, are called 'repositories'. There are hundreds of thousands of free programs to play with, but you can search by category. One of my favorites is 'redglass cursor' which you can download when you're configuring your cursor in 'Appearance' menu option. You'll see what I mean when you play with 'Appearance' options. 
Mint will recognize your sound card and motherboard, and monitor. All your changes and configurations store on that external drive/stick as if it were an extra internal drive. So now you can use it on any machine, in hotels, at your friends' houses, without any damage to their machines. Again, since it remembers YOUR monitor and YOUR machine, it will run ever faster each time it's plugged into YOUR machine. But when you plug it into another machine, it redetermines what drivers to use, keeping YOUR information intact as well. So after awhile, if you use only certain machines regularly, it will 'remember' them all and boot quickly.
And best of all, you can use it to do XP rescuing and housekeeping, mass copy your XP stuff, write to DVDs (which XP cannot do), clone and backup in ways XP cannot do, etc. You'll like that. Linux can even run some XP programs directly, but that's a lesson for another day. 
Hope this helps. Yell at me if it doesn't!
Edited by brainout, 24 July 2015 - 02:03 PM.