There is a known bug with the install of the Oracle SOA Suite on Windows Server 2003 whereby the service required to run the Oracle Application Server is not installed (bug note 423366.1).
To fix the problem you can create the service yourself using sc.exe.
sc create Oracle<Home Name>ProcessManager binPath= "<Home Path>\opmn\bin\opmn.exe -S " DisplayName= Oracleoracleas1ProcessManager
Replace <Home Name> with the name of the Oracle Home (where the application server is installed which can be found in the registry HKLM/SOFTWARE/ORACLE/Key/ORACLE_HOME_NAME), and <Home Path> with application server the install path. Note that the <Home Name> is case sensitive, also note the space after the binPath and DisplayName options - these are important!
This will create a service named "Oracle<Home Name>ProcessManager" which you can configure to auto start.