I have never had to start the database manually on my windows HQ server. It is a dependency from, and starts automatically, when you start the HQ-Server service.
Did you install by running our installation batch file in a command prompt with -full?
Based on the limited knowledge all I could suggest is this. (only if this is a new install)
1. Re-run your "setup.bat -full"
2. Pick server installation
3. Answer all questions and let installation complete
4. Once install is complete close the server
5. Run "hq-server.exe -i" to install the server as a service
6. Go to your Services and right-click Hyperic HQ Server and click Start
7. It should start the server first and then the database
8. Verify that you can log into the HQ interface.
As I typed this it started sounding pretty thin to me, but hope it helps. If you did most of this but didn't finish, i.e.-didn't install as a service, pick up at that point and finish up.
Also, if there is some reason that I don't know about where you would rather start your database manually, please disregard this post entirely.