It's the fill valve. Does yours look like the one below?
(Ignore the cap color, I'm just talking about the general style.)
If so, you can fix it by replacing this little cap inside it:
It's Korky Part R528, and it's available at HomeDepot, among other places:
http://www.homedepot.com/p/Korky-Toilet-Fill-Valve-Replacement-Cap-R528CM/202666007
Here are the instructions on how to service your fill valve, and you can swap the cap when you do so.
If you don't have this style of fill valve, the valve isn't easily-repairable, and you need to replace it with the Korky 528MP. (Toto uses 3 different manufacturers' valves, and they are entirely-interchangeable, but the Korky is easiest and cheapest to fix.)
You can get the Korky 528MP MaxPerformance fill valve at Home Depot and online.
http://www.homedepot.com/p/Korky-QuietFill-MaxPERFORMANCE-Fill-Valve-528MCM/203145423
You want the MaxPerformance one, with the silver top, not the white one or any other color. The others won't properly-refill the bowl. You can also replace it with the Toto TSU99A.X universal replacement fill valve, which is a Toto-branded Korky 528MP, made by Korky for Toto, that costs more but is essentially exactly the same.
It should take less than ten minutes to change the valve.
Here's how to install it:
Now, you also say that it's making the noise without flushing. This probably means that there is some water leaking out of the tank, and it's making a noise when it goes to refill that water leaking. The easiest way to check is to turn off the water to the toilet, mark the water level with a pencil in the tank, and come back 3 or 4 hours later and see if it has receded. If it has, then you need to replace the flapper, which is a 30 second process. There is an adjustable 3 inch Korky flapper that you can also buy at many stores, which will fit perfectly. However, it's easier to just get the Korky Red Fits Toto flapper, which you won't have to adjust. Your toilet uses the THU331S Toto flapper, which Korky made for Toto, and this one is identical -- it's the same flapper in a different box:
http://www.homedepot.com/p/Korky-3-in-Toilet-Tank-Flapper-for-Toto-G-Max-2021CM/202666003
Both products are available locally and at many hardware stores, as well as at Home Depot. Don't let some dude in Home Depot or at the hardware store tell you any differently about what fits or works. The number of times we tell people what to do and then get contradicted by these know-nothings is amazing, as is how patient we are when people ignore our advice and then come back when the problem remains unfixed despite the fact that the smock at HD or Lowe's, who "clearly" knows more than we do, told them the real deal on what to do.
Just do this, and you will be fine.