Edit: Whoops! I was talking about the actual NES. I didn't realize this question was about the NES Classic. My bad!
Sounds like the lockout chip is resetting the system every second.
Almost always, when an NES is having issues, it's because there's a bad connection from the game to they system. Try these steps:
- Clean the game. Open it up and use an eraser to clean the contacts. If it still looks dirty, use 99% isopropyl alcohol (IPA) and a Q-tip.
- Your 72-pin connector may be bad. I've never had luck cleaning them, but you can try it. Most reliable fix is to get a new 72-pin connector on ebay for $7.
- Every once in a while, the contacts on the motherboard can get dirty. This is less likely to be the problem, but you can try it. Pull the 72-pin connector off the motherboard and clean the contacts the same way you cleaned the game cartridge. If you go to the trouble of cleaning the motherboard, you might as well use IPA and get it really clean.
If this doesn't work, you could try disabling the lockout chip. It's easy to do, you just cut one pin of a certain chip on the motherboard. Usually you only need to do this if you frequently see the game actually start up, but restart and restart. If you see a blank screen when it constantly restarts, it's probably just dirty connectors.