Hi
I've just tried to reinstall DP1.5 using the serial number and registration code given to me from my account.

On opening the instrument, I'm asked to register it, but when I do the website kicks back with an invalid serial number message.

What to do now?

Look again in your Cakewalk account, if you upgraded to a newer version of Sonar anytime after you received your Dimensions Pro, then the new serial number and registration number will be listed there as well.  The same happened to me.

Try installing with administrator permissions.

Follow Jesse's advice and eph if administrative privileges are an issue.
 
Installing or reinstalling Dim Pro has always been a cluster fork. You are not alone in this frustration.
 
You got the Sonar packages and the independent package with different serials. Major mess. Then the nightmare of the libraries if you try to install them against a blocked installation.
 
Get to your Cakewalk account and there will probably be confusing multiple serials and registration codes. Go through them one by one, and one should work. Should not be this hard, but can predict that nothing will be invested to fix it for anyone else dealing with this problem.. As long as this can get you up and running before the Titanic sinks.
 
John