Original NESes seem to still work great, with one exception: The 72 pin connector (what the cart actually plugs into) is usually the first, and only, thing to go. My understanding is that it is TIME based, not usage based, so picking up an old one might still give you some issues.
If you start having issues that make you want to blow into the cart and into the NES to fix them, (IE gray screen, flashing power, and maybe if you fuss with it for 15+ minutes, a garbled into screen), you need to replace your 72 pin connector. You have to unscrew almost everything, and use a little bit of force to get the old 72 pin connector off, but it's early 80s tech, so any amateur electronics tech will probably be able to do it.
Any used-game store that stocks NES cartridges will almost CERTAINLY have brand new 72 pin connectors for somewhere in the $10 range, my local one offered to install it for me for another $10 (did it at home with no problems). As for NES 2s, I don't think any place even HAS replacement parts. The original is probably a better investment! Mine works just like new after replacing that part.
And for batteries, well, I know my old Wizardry cart still works fine and I think my Zelda one still works as well. They are not ALL guaranteed to be dead by any stretch, there is probably a lot of variability. (I ran into a dead Wrecking Crew cart like ten years ago!) I wonder if it's possible to replace the batteries...hmm.