Cannot restart IIS 7.5

I have problem with 32 bit ASP.NET application which causes IIS to stop responding.

Server is Windows Server 2008 R2 Datacenter x64 with latest updates.

In more detail:

1. after some time I cannot log in to ASP.NET application
2. its homepage loads fine, but when I press "login", the page keeps loading...
3. restarting web site won't help
4. restarting IIS helps but the problem is that I cannot restart IIS (it does not respond) but need to manually kill w3svc.exe (it has RAM usage cca 30 MB and CPU utilization 0-1%)
5. application has own logs but they do not indicate a thing
6. no errors/warnings in Event Log.

I had the same problem on Apache + mod_dotnet on Windows platform.

It's very likely the problem is inside the ASP.NET application. I've just enabled Failed Request Tracing.

Can you recommend me an approach to narrow down the problem (except debugging the app - I am not developer)?