Typically 1603 errors are hard to diagnose. But generally you can run down a list of things and usually get it.
Here's where I'd start:
1. Make sure you don't already have any other vertical flavor of AutoCAD 2013 already installed before installing BDS2013.
2. Make sure you have local administrator privileges. Sometimes Office updates switch you to Debugger User, etc. So verify you are local administrator. In fact, you might even try logging in as Administrator or running the installer as Administrator.
3. Make sure UAC is disabled completely
4. Make sure anti-virus is off.
5. If you are installing from media (DVD or USB) copy the contents to a folder on your local hard drive and install from there. If you are installing from network deployment, make sure you have full read/write to the share and folder permissions and do not make it a silent deploy.
6. Do not add the service pack during the install. If prompted, decline. Add the service pack afterwards.
These are the typical things to try. Generally one or more of them will get you where you need to be.