Toilet occasionally not re-filing?

Hi

Since I moved in to my house four years ago one of the toilets occasionally doesn't refill without giving the tank a shake/nudge. It was doing it once every few months but recently does this once per week. I am assuming something is getting stuck in the cystern when I press the flush and then dislodges when you give the tank a shake. I would just look inside but it's one of those inbuilt press flushes so not sure if it is this easy. I am to attempt a self repair but not 100% certain what is likely to need repairing, cleaning or replacing? Any ideas...

Thanks....

When you say doesnt fill does the water constantly run into the toilet bowl? Or no water enters the cistern ?

No water enters the cistern...

Just fit a new fluidmaster ball valve. Your old valve is just getting stuck through age