With "four servers in the farm" I guess you have 1 SQL Server, 1 App server and 2 Web Front End Servers. To deal with a single server failure you need to know which server your actually browsing.
You can do this the hard way, and turn off one of the WFE:s as in shutting down all web sites in IIS. Then you know for sure which server you're on, and can access logs knowing for certain what server caused it.
You can also do it the soft way and browse to the server IP-address since its unique for every server in your domain. When your accessing a server through its IP-address, you know which server replies on your request and can start looking for errors form there.
A few tip as you continue:
- Do both servers have the same SharePoint version, patch and upgrade in place, and have PSCONFIG been run on both servers since last patch session?
- Make sure web.config are equal on both servers
- Make sure you're using the same app pool account on the web site on both servers
- Check the hosts-file and remove pointers to this server for the actual web site. Mapping should be made on the DNS.
- Check the hive content on the servers and make sure they are equal
- Are windows features, services and possibly other third party components in place on both servers and configured equal? (I know this is a tough call, but if you're done with 1-5 you're running out of options).