First of all, that task is impossible without previous knowledge. A project like that could easily take weeks if not months, since you rarely can find somebody in an organisation that can definitely say that something isn't needed anymore. Futhermore, you can never truly trust logs for that task either, since proving that nobody is using some resource can be rather hard, what if that server for example only is used every other month?
But, what you can do is catalogue all servers that are running software or operating systems that are end-of-life due to no longer being supported by the vendor.
Start with the operating systems, anything older than Windows Server 2012 are not supported by Microsoft anymore, and should have been replaced already. Windows Server 2012 is also already in extended support, so it's should also be phased out within 2 years.
Then you just need to go through all servers with supported OSs and check if they are running any software that's EOL, for example MS SQL Server or Exchange. Anything EOL should again be upgraded or phased out if no longer needed.
Microsoft products EOL dates can be checked here (Windows Server 2003 for example)
It's also a lot more effective to get responses from departments if you aren't asking them what something is for, and instead tell them that by this and that date the following servers will be terminated if nobody has no further use for them.
If you still want to go down the route of log analysis, Splunk has a free tier that allows you to import quite a lot of data 2 times per month if memory serves, and they also have a quite good toolkit for log analysis on Windows servers.