It could be a host of things really. I've very familiar with vintage game consoles, so I'll try to help a bit...
- First thing you should do is clean the contacts on the game cartridge and inside the console. You'll need Isopropyl Alcohol for both.
-- For the game cartridge, use Q-tips. Dip them in the Isopropyl Alcohol and rub them back and for across the goldish colored contacts (the part that plugs into the console). If the Q-Tip gets dirty, use a new one. Keep doing this until the wet Q-Tip can rub across the contacts without picking up any dirt or gunk.
-- For the console contacts (the slot the game plugs into). It may be helpful to take the console apart. Just remove the screws on bottom and take the top portion off. Once that's done, grab yourself the Isopropyl Alcohol, a credit card, and some type of decent cloth (I've found a scrap from an old t-shirt works well, but you'll just want something that won't leave a bunch of lint behind). Wrap the cloth around one end of the credit card and pour a bit of Isopropyl Alcohol on it (might be less mess to pour a little alcohol in a bowl and dip the cloth). You don't have to drench it, just wan to get is damp. With the damp cloth wrapped around the credit card, insert it into the cartridge slot on the console and pull up. Do this repeatedly and wipe off any gunk that it pulls out each time.
Isopropyl Alcohol dries pretty quick and won't leave residue behind, so give reassemble the console if you took it apart and try it again. If you're still having problems, it could be the cords or the TV. The sad thing is that a LOT of newer HD TVs won't play vintage game consoles correctly. You'll need a special cable or some confangled converts. Fortunately, there's a couple different companies that make converter cables for vintage consoles. I have and sue the HD Retrovision brand and they work awesome. Not too pricey either. Or, you could just try and find an old, tube style TV. Craigslist in your area probably has a few for free.
As for the controllers. It's pretty hard to completely kill a vintage controller and usually, all you need to do is take it apart and clean the contacts where the buttons meat the circuit board with Isopropyl Alcohol and a Q-Tip. Sometimes you'll need to replace the rubber contact pads and replacements for those can be found various places online.
