The wii typically uses just a composite input as well, so that does make sense why it was working.
If looking for a replacement, I recommend sticking to the name brands, which tend to be the most reliable, such as Panasonic, Samsung, LG. The “off brand” sets just aren’t worth the savings, they have high failure rates and are poorly supported if parts/repairs are ever needed. Example: http://amzn.to/2dYWKT8
If you happen to be a costco member (or know someone who is) I'd suggest buying it there. They tend to have very good pricing to begin with, but will also double the factory warranty to 2 years instead of 1, and they have a square trade extended warranty you can buy up to an extra 5 years for $50 or so which is well worth it. Wherever you buy, I'd highly recommend the square trade warranty (the "store brand" warranties aren't worth the paper they’re printed on). You can get that here, no matter where you buy the tv: http://bit.ly/1fDPJ99
As a side note, I would not personally bother with a "smart" tv. You'll pay a premium for those features which end up being slow and glitchy and aren't well supported. By contrast you can spend 30-100 on a roku, roku4k, fire tv, htpc or smart bluray player and get all the same functions and many more, with better performance and lower cost.
Best regards, ***** ***** again for the news,