Help needed! Car won't start

[mf4361]

Hello and help, I have a canadian 2007 Sedan.
My car won't start in the afternoon, not even a sound of cranking. The dash faintly flickers. It was fine this morning and lunch time and no sign of any problem.

I checked the battery it's showing 12.4V, but measuring from the interior 12V power source shows 4.7V.

It did shows some weird moments where it doesn't responds when i turn the key (not even lights). But back to normal after I take out the battery terminals and put it back

I am guessing the starter problem? I havn't got a chance to check the starter fuse but I will soon (I have to leave it in the local coffee shop and have my colleague give me a ride :()