If you ping both the name and IP address of a host and they are both successful but the user is still unable to access the application where is the problem most likely to reside?

In a question this general, the only way to answer without pages of nonspecific information about potentially hundreds of issues is to say: Most likely the problem lies with the host or with your use of the host.

Trouble shooting questions to ask to get started:

Can other people access the application?

If yes, then it is on your end.

If no, then it is on the host end.