Those Famicom Twin (AKA FC TWIN) systems are garbage, steer clear away from them. They not only have sound bugs, but will not play everything correctly. Don't get me started on the NES part either, that portion is just as much junk as the SNES part. The NES portion holds on to the carts so hard, that you think you are going to rip the PCB out of the cartridge when you try to remove it! That portion also has sound bugs and does not play everything as well.
They are a complete waste of money, and a lot of independent game stores that carry the things lie to their customers saying that they play everything and that there are no problems with them. It's a cop out because these same stores usually carry used decks, and either can't keep them in enough, or people don't want to trade them in for as little as they give on the stuff. It's an alternative to their cheap customers that don't want to pay as much as they are charging for a real SNES. Also, the same stores are usually getting those Famicom Twin things for around 20 something $, and selling them for 55-60$. That's a nice markup there. They usually try to sell those to people first and foremost, because they can simply just send it back to the distributor if there are any problems. Same stores also only give credit back, so no matter if they have to return it to the distributor or not, they issue a credit slip and they have the customer's money.
Not sure what everyone else's deal with the SNES Jr. (the 2nd model SNES) is. I have never had any problem with one personally. They removed the RFU out (big deal), the cart ejector, and the power light. I always used the proprietary Video/Audio out that is the same on the SNES/N64/Gamecube, as I have both AV and S-Video cables for that port. Not sure what everyone is talking about on those models not having S-Video out, as I have never tried using my S-Video cable on one, so I can't vouch for that. I only have the larger 1st models, but it has nothing to do with not liking the SNES Jr.
When I was in New York state for a year, I had one die on me, and I never figured out why. I had another one I got from someone up there start acting funny as well. Then the one I picked up off of eBay to remedy all of this, ended up being shit (had to get a refund from the guy over the whole thing). I think it had something to do with the electricity and grounding possibly, but either way, everything is fine back where I live at now, so I'm with no answer.

Either way, regardless of what you get, make sure you get a real system. Don't waste your time with those borderline pirate dual systems. They are junk. If you really want to have a SNES that plays both, get one of those SNES to NES adapters that were made years ago. Those had better NES compatibility than these new things do.
Best of luck.
EDIT:
BTW, did you check your AC adapter on another system???Make sure that is not what the deal is. You can get AC's cheap, much cheaper than buying a replacement system.
Here are some eBay links for you. Looks like you can get just a deck for 25-35$ plus shipping, around double for one with games and other stuff. Just be picky and look around before jumping. I have not dealt with any of these sellers either, just being nice and posting links of the REAL systems. These are just about half the ones that were Buy It Now!, you could probably find some bid ones play the wait out game, possibly getting a better deal, but it's always a gamble.
http://cgi.ebay.com/NINTENDO-SUPER-SNES-SYSTEM-CONSOLE-WORKS_W0QQitemZ140202095432QQihZ004QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/NINTENDO-SUPER-SNES-SYSTEM-CONSOLE-WORKS_W0QQitemZ140202655194QQihZ004QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SNES-SUPER-NINTENDO-PLUS-2-GAMES_W0QQitemZ220194094879QQihZ012QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SUPER-NINTENDO-SNES-SYSTEM-MINI-SPEC-EDITION-7games_W0QQitemZ300193141843QQihZ020QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SUPER-NINTENDO-GAME-SYSTEM-SNES-2-CONTROLLERS-4-GAMES_W0QQitemZ370016127769QQihZ024QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SUPER-NINTENDO-SNES-system-complete-SUPER-MARIO-WORLD_W0QQitemZ180210606021QQihZ008QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SUPER-NINTENDO-SNES-SYSTEM-MARIO-WORLD-MORE-WOW_W0QQitemZ120213806738QQihZ002QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SNES-Super-Nintendo-SYSTEM-2-CONTROLLERS-GUARANTEED_W0QQitemZ290200301668QQihZ019QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/OFFICIAL-Super-Nintendo-Console-Original-SNES-System_W0QQitemZ200194748332QQihZ010QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SNES-Super-Nintendo-SYSTEM-CONTROLLER-GUARANTEED_W0QQitemZ110216962583QQihZ001QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SNES-SUPER-NINTENDO-console-9-games-lot-MARIO-WORLD_W0QQitemZ110218682172QQihZ001QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SNES-Super-Nintendo-System-COMPLETE-MARIO-is-MISSING_W0QQitemZ280195231449QQihZ018QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/SUPER-NINTENDO-SNES-SYSTEM-W-CONTROLLER-GUARANTEED_W0QQitemZ280195420127QQihZ018QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/Super-Nintendo-SNES-System-with-Controller_W0QQitemZ150210304840QQihZ005QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/Super-Nintendo-System-4-Games-SNES-Console-Hookups_W0QQitemZ300194236023QQihZ020QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/Super-Nintendo-System-5-Games-SNES-Console-Hookups_W0QQitemZ290201864953QQihZ019QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/Super-Nintendo-SNES-Console-System-2-Controllers-1-Game_W0QQitemZ260207389742QQihZ016QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemhttp://cgi.ebay.com/NINTENDO-SNES-SYSTEM-w-7-GREAT-GAMES-L-K_W0QQitemZ130192980800QQihZ003QQcategoryZ62054QQssPageNameZWDVWQQrdZ1QQcmdZViewItemBest of luck.