Hi!
This heavily depends on the Oracle installation on your system where you have reinstalled the PLSQL Developer.
If you have a single & clean Oracle Client x86 installation PLSQL Developer should find the tnsnames.ora itself. But this isn't the case it seems.
If you have more Oracle Homes (Clients, Servers, Instant Clients) or a messed up Oracle environment on you box then you can try to choose the right Oracle Home manually from within the PLSQL Developer Preferences->Connection->Oracle Home.
You could also try to set the right Oracle Home via "Oracle's Home Selector" if you have Oracle