Did this problem happen suddenly or did OE slow done over a period of time then stop altogether? If it slowed down, the problem could be bloated .dbx files (where your e-mails are stored). Even when you delete e-mails, OE does not clear them from the .dbx files. There is an option (under File I think) which tidies up these files. There is also an Index file stored in the same directory which can cause problems. I think you can just delete this file and it will be recreated (but best get confirmation from someone before you try this!!!)
A custom install should allow you to install only the bits you need, that is Outlook Express. Personally I wouldn't reinstall the whole of BT broadband - your Internet Explorer and Outlook Express components are not really part of your broadband set up only utilities to allow you to use the internet. Internet Explorer and Outlook Express are linked (so see Stuartli's post above). I suggest doing a search of your c drive for '*.dbx' (no quote marks) That should find any Outlook express files still on your computer. If you find any, double click one (try inbox.dbx if it is there). If you are asked for a programme to open it and Outlook Express is not listed (if it is, use it) browse to programme files, outlook express, msimn.exe - that is the outlook express programme. See what happens if you open it. If your dbx files are there you should not loose any emails, if not, you have already lost them! I am wondering about the reference to freeserve and your use of BT broadband. I wonder if there is a conflict??? Don't know why there should be.
Re. the link above, are you using MacAfee's Virus Scan?