Quick post: I was trying to connect to a 64-bit Oracle database using PL/SQL Developer. Despite ORACLE_HOME being set the right values and oci.dll available, PL/SQL Developer could not connect to the database.
Further probing indicated that the Oracle installation was a 64-bit one, and PL/SQL Developer is incapable of loading 64-bit version of oci.dll file. To fix this, download the 32-bit version of Oracle Instant Client, extract it to a directory such as \instant_client.
Next, configure PL/SQL Developer to use this version by clicking on Tool menus -> Preferences. Under Oracle Home, point to the location where you had extracted Instant client (\instant_client, in this case) and under location of OCI Library, point to the oci.dll file present in location where you had extracted Instant client ( \instant_client\oci.dll). Restart PL/SQL Developer and you should be able to connect now.