SQL Server and IIS do not play well on the same server. You may have to throttle SQL Server's use of memory on the box so that IIS is not memory starved. Search the KnowledgeBase site or Google the microsoft.public.* groups with IIS , SQL Server, and memory keywords.
This sounds reminiscent of a question in the microsoft admin test that I took years ago.
In order to narrow down if this is a SQL server problem, or an IIS/Application problem, you coudl get profiler running on the SQL Server to trace all error events. The output will be somewhat confusing, as Profiler will not give you the text of the error message, and some of the messages are actually "normal". I never knew how many "Object not found" errors Enterprise manager could throw.
With this trace, you will find any overt SQL error that the database may be having. Things like the application having timeout issues would be missed by this, as Profiler will only trace server side events.
In order to catch possible timeouts, you could trace for any statement that takes more than 30,000 ms. If you see a lot of these, then you could have either poor database performance, or lock contention.