Water running but not filling or no water staying in tank?

Running but not filling

your flapper isn't sealing.

tjdabomb is probably right. This means:

1) you need to check to see if there is anything stuck to the sealing part of the flapper or the porcelain rim it bears against that might prevent complete sealing; or

2) you need to check the chain or whatever it is that connects the flush lever to the flapper (sometimes they get a kink in them and the flapper doesn't go down all the way); or

3) you need to get a new flapper ($5).

Toilets are pretty simple,,,you should be able to prove to yourself that the flapper is at fault by pressing down on it and forcing it to seal: the tank should fill up with your hand holding the flapper in place (don't worry...the water is clean!).

Please report back after you investigate further.

(One other less-likely possibility: I just fixed a neighbor's toilet with this symptom. The nut on the inside of the tank that holds the flush handle in place was a little too tight and the handle would sometimes stay depressed, so I backed it off about a quarter turn so it could move easily and return to the normal position.