instead of mapped drives, can you use fqdn?
the who is the app pool identity running under?
also, which user are you intending to have access to the shared drive? the impersonated end-user? network service? the app pool identity? you have to decide this first and verify those permissions on the shared folder. if your intention is the impersonated end-user you may have to set up delegation/kerberos for multi-hop credential passing.