I don't have nearly 4,000 - that's a ton of games. Good luck playing them all, I can't even play the 500 or so that I have.
It's taken me about 15 years to collect 500 games.. just a few, here and there, garage sales, thrift stores, ebay, etc etc. I have rarely got a huge lot except for the 3DO lot I aquired recently (with 57 games). It's more impressive when someone has built up a collection over many many years a few games at a time, than it is with someone that buys 100 game lots on ebay constantly.
I've also got rid of many games as well, I'd probably have 1000 games if I never got rid of any of them.
Storage space sucks, specially for controllers, a/c adapters, a/v cords, etc etc. Is there any one good way to sort through all that mess? I have controllers in one box, cords in another. But I still have to empty the box when I need to find something.