I too had problems with earlier Sybase versions on windows 2003. Martijnvs is most likely right, you'll need to apply an EBF (upgrade) to your installation for it to start on Windows 2003. If you start your server from command line and not from a service you'll see that it works just fine.
That said, there is also a problem with Windows and Sybase if you try to allocate more then 2Gb of memory, you have to put the /3G switch on in the boot.ini, but since you are running a new install I'm assuming you've left memory alone.
Also check the <sybase install>/ASE-12_x/install/errorlog file (in earlier versions this was <sybase install>/install/errorlog), it may tell you more about why Sybase doesn't start.