Toilet flushes fine. Tank does not refill, unless you turn on the sink faucet (located right next to toilet) for just a moment. Then it refills like normal. This happens more often than not.
Any thoughts? Thank you :)

I don't know if this is the answer but I would check for a shutoff valve on stool...

Children like to turn things, maybe one of them decided to fix the stool

You should be able to open and close it, make sure it is open

Turning counter-clock wise should open it, if this isn't the problem

The fill valve in the toilet may need fixed or replaced

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What type of ballcock to you have, Float ball on a rod or can on a wire?

I can see where Tom is going. I think your ballcock is hanging up and the pressure change when you open the faucet is enough to unhang it.

Thank you for your responses/suggestions
Sorry if I don't use the correst terminology, but I do NOT have the floating ball type. There is just a verticle tube (Fluidmaster 400A) with a larger black piece towards the top of the column and a gray ~3/4" wide ring toward the bottom and of course, the tube that gets the water sprayed into it.
I believe the water is turned on, because sometimes it works like it is supposed to.
Looking forward to your suggestions.
Thanks again

You, indeed, have a can on a wire FluidMaster ballcock. Shut the water off under the tank and press down on the top of the ballcock and twist counterclockwise. The top should the4n pull up and reveal a neoprene washer with a small hole in the middle. This is the seal. Pry it out and replace with a Fluidmaster #242 replacement seal. Now hold a wash cloth over the open top and turn the water back on for a few seconds. This will flush out the supply and ballcock body.l Reinstall everything, turn the water on and give it a flush. Work better now? Regards, Tom

I bought the whole assembly because I didn't know how old it was. My son installed it under my husband's guidance. Seems to work . Thank you !
On Saturday, we will replace the washer in the shut off valve if that is still dripping :(

No no no!

You've got it all wrong!

This is a safety-interlock device to ensure that you (at least pretend to) wash your hands!

:) :)