Let's say that the richest man alive decides to pour unlimited funding into making a perfect Nintendo 64 emulator.
This emulator can require 100 data centers full of ultra-expensive servers for processing. It can cost any amount of money. The only constraint is that it cannot take unlimited time to make. Let's say that they get a maximum of two years.
When I say "perfect", I really mean perfect. The pickiest, most hard-to-please retrocomputing snobs in the world will be hired to try this emulator out by having them repeatedly blind-test different Nintendo 64 + CRT "stations". 50% of these have a real Nintendo 64 (behind a cage) and the other 50% have what looks like real N64s, but they are actually hollow and just contain the "glue electronics" for the controller, power cord and the TV signal cable; inside, they are wired with a fiber cable to the next room where the hardware for the emulator resides. (Or where it begins, assuming it requires so much space.)
Other than trained human eyes, it will go through a number of tests to try every single game extensively and make sure that the exact same signals are sent back from the emulator as a real N64. If there is natural variance, an average is calculated from multiple real N64s and compared to what the emulator sends back.
Essentially, I'm asking if there is something fundamentally impossible with this, or if it's just that even our strongest home PCs are way too weak. Since any amount of computing power can be used in this scenario, the question is all about the software/logic.
Of course, they are not allowed to just replicate the hardware of a N64, or to invent a new computer platform which is extremely similar to a N64. It has to actually emulate it in software, albeit with extraordinary hardware resources. (Probably, but not necessarily, x86.)