Hi:
I don't know what other information to provide.
Thanks for your help!
Do you know the brand of toilet and approximate age? One-piece or two-piece? Alternatively if you can get the model number from the tank or tank lid, that might help, too. These would help us know if it's a 3" or 2" flush valve, for example.
You had the right instinct to replace the flapper, and it may still be the flapper; you might just need a different one or different style.
Alternatively, as was suggested above, you might have some leakage around the seat where the flapper seals, and cleaning that area (or installing a new rubber seal around the edge of the seat that meets the flapper -- there is a quick and easy kit for that and it's the easiest of the available fixes) may solve the problem before we get into the kind of toilet surgery mentioned above.
To see if it's leaking around the flapper still, turn off the tank water while marking with a pencil or eyeballing where the water is. If the tank is lower a few hours later, you have a leak most likely between the flapper and the flush valve. If it's a generic toilet, one of the experts on here recommends the Korky flapper. I have been using the red Korky plus universal flapper with the adjustable cone very successfully, but it also comes without the adjustable feature for a buck or so less. If it's a more unique toilet, but still uses a flapper, look at Korky.com to see if there is one more suited for your setup, or even call them and ask. They are very, very nice.
If you have a crack in the flush valve or want to make it take a more standard flapper, you don't need the whole kit with the fill valve as well, you just need the flush valve, and you might consider the Korky universal adjustable one, which I have on two of my toilets. It's relatively-easy to install, but you still need to be at least a little handy, because it involves removing and reinstalling the tank. That's why cleaning and/or putting a new ring seal on the existing flush valve is a step that you should try first after you check whether you are using the right flapper.
Also, check the tension on the chain between the flush handle and the flapper. There should be minimal slack, but there should be at least a link or two of slack, so the chain isn't holding the flapper off the valve. Believe it or not, there are some toilets (I have one), where the flush mechanism is such that when you put the lid back on, it actually depresses the flush mechanism part way, so you have to leave a few extra links in the chain to compensate. It's unlikely that your toilet does this, but if you have a pushbutton flush, then it might.
Those are all the thoughts I have without knowing more about the toilet. Good luck!