I am guessing that you didn't back up your database and site before upgrading the module?  If this is the case, you would want to manually change the Links Module version number in the database, and then reinstall the previous version of the module.

Please Note:  DO NOT run the query below without first backing up the database.

You would need to edit the value in the database itself.  However, I am uncertain if there are any side effects from doing this.  Run this query on the SQL page in the Host Menu:

UPDATE {databaseOwner}{objectQualifier}DesktopModules SET Version = '03.01.00' WHERE FriendlyName = 'Links'

Then, before you attempt the upgrade again, be sure to go the Host Setting page and click on the "Restart Application" link at the bottom of the page.

As far as backing up the database, the method varies from host to host.  If you do not have a web host and this is in a company, then your life is easy.  Ask your Network Administrator.  Otherwise, shoot an e-mail to your web host asking about how to backup the database.