First question is how much attention do you pay to the FM world? This has an impact on how many leagues you like to run. If you were happy with your 3 leagues then an upgrade really shouldn't be necessary except for maybe some new RAM.
I'm going to reiterate what everyone else said on the off chance you've browsed over it as being skint buying a new laptop in my opinion is unnecessary especially if you enjoy FM with 3 leagues:-
With you current system to speed it up:-
1. Turn detail level to minimum on any competitions you aren't playing in.
2. Turn off your antivirus (or add the relevant FM locations to your exclusions if you intend on surfing the net or avoid dodgy stuff if on FM and the web at the same time).
3. If you have a partitioned single physical drive then allocate the paging file to the partition you install programs to. Also make sure you have enough free space on the drive to accomodate the page file contiguously (all in one lump). Right click my computer > Properties > Advanced > Performance Settings > Advanced Tab and under Virtual Memory click change to see the Initial and Maximum size. Make sure you have more than this available. A good way to ensure this is to defrag your drive until you see a nice chunk of contiguous space available on the relevant drive (this might not be possible though, especially with XP defragmenter which isn't great). When you click on Analyze in disk defragmenter the green unmovable files are the pagefile.
4. Turn off the Disk Indexing Service (open my computer, right click the drive and untick 'Allow Indexing Service etc.). Let it do it's thing to completion. It might throw up some exception errors but just click the relevant button to continue (off the top of my head can't remember exactly which one but it'll make sense if it happens).
5. Open up Task Manager and see what if any processes you can turn off (any software stuff that isn't in use like iTunes, Quicktime, etc.). Google is useful to find out if it is safe to do this. Do this with FM open and see if something is consistently competing with FM. Anything untoward may point to a virus.
Improving your system for what you want:-
1. Digital photo storage. Depends on the camera you have and the size of the files it creates, as well as to what extent you intend storing. Reliability is the issue with files you intend to keep indefinitely and you'll find different people have different opinions. Me I find CDs/DVDs to be an issue with my laptop so I prefer an external hard drive. There's a good offer on amazon at the moment for a 500GB Western Digital for £60 (500 GB might be overkill for what you want but too much is better than too little, and at that price it is a very good deal).
2. Playing FM. Your processor should be more than capable of running a reasonably sized FM save game so your best bet is upgrading RAM. Different laptops mean different costs and possible configurations so do a little googling to find out the score.
3. Buy a replacement keyboard.
Just a sidenote that your fan going mental is not necessarily a bad sign as that is what they are designed to do. See Serpico's post on overheating. Also re your laptop shutting down: Does it only happen when playing FM or has it happened under a light load like surfing the net? Download Speedfan
http://www.almico.com/sfdownload.php and check the temp of your CPU when running FM. Do a google search of your CPU's operating temperature range to check if it is within the reasonable range.
Apologies for repeating what has been posted but given you say you are skint spending on a new laptop isn't a necessity in my opinion. Also it's worth noting that 'slow' is subjective. I'm running England BSS up (so 7 leagues total) on a 1.6 GHz Pentium M and 512 MB RAM (same as yours), set detail level to none and it runs ok for me. But ok for me might be painfully slow for someone else as if you find 3 leagues slow on comparable specs then my idea of ok may well be like waiting for hell to freeze over for you.
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