Try a new identity and see if the problem persists:

You may have a damaged identity especially if it is the default Main
Identity. File | Identity | Add New Identity. Create a new one and test it.
If all is well, you can import your messages and Address Book from the old
identity and delete it.

How to Create and Use Identities in Outlook Express
http://support.microsoft.com/?kbid=209169

If still no joy:

Hyperlinks do not work in Outlook Express after you upgrade to Internet
Explorer 7:
http://support.microsoft.com/kb/929867

If still no joy, for IE6 & IE7:

From:
http://www.fjsmjs.com/OE/nolinks.htm

If nothing happens when you click a link:
Open Windows Explorer, or the Control Panel.
Go to Tools | Folder Options | File Types.
Scroll down to [NONE] URL:HyperText Transfer Protocol (NOT URL:Internet
Shortcut) and select it.
Click Edit or Advanced, depending on your Windows version.
Select 'open'.
Click Edit.

"Application used to perform this action" should read:

"C:\PROGRAM FILES\INTERNET EXPLORER\iexplore.exe" -nohome (Check the path to
iexplore.exe to make sure that is correct and use the double quotes.)

DDE should be checked and in the boxes below it you should have:

#1:
"%1",,-1,0,,,,
#2
IExplore
#3 (blank)

#4
WWW_OpenURL

URL:HyperText Transfer Protocol with Privacy should be the same.

Sometimes it is necessary to uncheck Use DDE.