instead of mapped drives, can you use fqdn?

 

the who is the app pool identity running under?

 

*edit*

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.