Pretty sure modifying copies of Windows so that you are circumventing the EULA constitutes a crime in of itself.

Assume he finds the modified copy of Windows on the ground. (Ie someone anonymously took out the check.)

In that case, no, Microsoft would not be able to do anything to someone who found a Windows DVD modified to remove the EULA check:

1. Copyright would not be involved because copyright cover the reproduction and distribution of content. You did neither. It'd be the same if someone photocopied a book and you found the copy on the ground. You might argue that "well, you need to copy the software from the DVD to the system". If that's a problem, imagine that the mysterious individual also somehow installed the OS on your computer without your knowledge.

2. Patent law doesn't apply because patents (in theory) cover the application of techniques and technologies. Patents are irrelevant to end-users.

3. As stated before, the EULA also doesn't apply.

IMO, applying patents to living organisms is completely bogus, conceptually. It'd make more sense if the genetic information of the organism was copyrighted. Then it would make some sense to talk about unlicensed copies being made, although it'd still be rather tenuous. Copyright wasn't thought for self-replicating and randomly-modifying data. Has a law been broken if a disc undergoes mitosis? How many words would you need to change for a book to no longer be considered the same?

> In that case, no, Microsoft would not be able to do anything to someone who found a Windows DVD modified to remove the EULA check [...]

They would certainly be able to do something about that person, if said person would start distributing copies.

Sure, but that's why the example only says that the person installed the software.

Also, question: What if, unknowingly to this person, the OS had been modified to act as a BitTorrent client and seed copies of itself?

I think there's stuff like Acting in Good Faith that comes in.