The symptom: Oracle 10g R2 Installer shuts down immediately upon pressing the Next button during Oracle patch install. It does not install the patch and does not report any errors in the logs.
The scenario: This occurs in a 64-bit system with Oracle 64-bit database and Oracle 32-bit client on a MS Windows 2003 server with SP2. On a 64-bit system, there are two Program Files folder structures, one for 64-bit systems (Program Files) and one for 32-bit systems (Program Files (x86)). When Oracle installs 64-bit products, it updates the inventory in the Program Files structure. When Oracle installs 32-bit products, it updates the inventory in the Program Files (x86) structure. However, there is only one registry entry pointing to the location of the inventory -- in the 64-bit area of the registry (this is the main registry; the 32-bit registry is a structure called Wow6432node). Apparently, when the client was installed, it replaced the location of the inventory, pointing Oracle to the Program Files (x86) structure. So, when the installer went to run the patch, it was pointed to the wrong inventory; it thought there were no database products installed. The installer, seeing it apparently has nothing to do, exits when you click on Next. (The clue was the 64-bit installer said there were no Oracle products installed on the machine.)
Immediate solution: Change the registry entry to point to Program Files.
Better solution: If you are doing a new install, apply the patch after you install the database and before you install the client. This will avoid other problems with the patch install involving the TNS listener.
I am posting this because I could not find anything on this forum or in Google that helped. Hopefully, this posting will help someone else resolve the issue more quickly than we did.