Jenna ........ the chunk on the left is the inlet valve assembly with a bottom entry (oo-er) for the mains to comein. The square boxy bit is probably the float. This rises with the water level, then hits the valve and shuts it off when the level is right.
As you know ......... the assembly on the right is the flush system. You push the button, it lifts something and the water flushes out ...... simple as that.
If it sounds different when it's filling, I guess the inlet valve has gone faulty. Not enough water, so no flush.
The inlet assembly can be dismantled. Often, it's just a piece of dirt that's obstructing the valve. Also, if I've identified the float correctly (they keep coming up with different designs ....... very confusing) then it shouldn't be so high if there's no water in the cistern. Maybe it's stuck?
All you can do is dismantle the inlet bit and fiddle with it. Otherwise it would have to be replaced. Simple 10 minute job to fit, but could take all day trying to find a replacement.
Note the brand name of the WC, and maybe show the pic to a good plumbers merchants to see if they can supply one.