Just solved it for me with these steps...
1. Uninstalled all Oracle products.
2. Deleted the Oracle directory, (since the Oracle uninstaller did not do so).
3. Visited here http://www.oracle.com/technetwork/database/10203vista-087538.html
4. Downloaded the appropriate version for my 32-bit Windows 7 of the "Oracle Database 10g Client Release 2 (10.2.0.3)".
5. Installed using the Administrator option set (probably doesn't matter which install option set you choose).
Noticed that during the install, the scrolling log section mentioned applying patch/fixes. So I'm guessing that the original Oracle 10g client connection software that I installed was missing whatever this patch was...
Without even rebooting, I tested the connection using several non-Oracle tools and it now works. Hope that is a help.