My closed cords don't sing

I am really really wet behind the ears still...

When I play a closed cord, half of my strings don't sing - they just clink.

To get all the strings down on the frets so they sing I need to place a lot of pressure down with my opposing thumb providing the tension to the point that it starts to hurt.

I've discovered that if I rotate my pointer finger a bit it helps, somewhat...

Is this normal for a beginner? Any tips on how to resolve this problem?

thanks!

Very normal. It's all a matter of applying the right pressure without straining yourself or muting the strings. Just try changing your hand position until you can get it to sound right. :3

Check exactly where you are pressing down on the frets. I always thought it best to press just above the lower fret, when actually you get a cleaner sound when you press exactly in the middle (and it requires less effort too!).
Press on my man!!!!

It's totally normal. It's beginner's pain so no worries Your thumb just has to get used to all the pressure. try resting the neck in the top part of your palm and press your thumb near the top (left, lookin from the front) of the neck

Don't fret, it may not be your fault at all. While it's normal to suffer some fatigue while you're beginning, it should by no means be as difficult as you describe. Have someone in the know check out your action for you. It could be that your strings are too high above the fret board, a common ailment more associated with less expensive instruments. A good set of strings can also affect playability.
Also learning good fingering position from the beginning will pay off big dividends in the long run. The bad habits you pick up in the first few weeks (using your thumb) can be tough to break. Carefully study finger position in some good books or videos.
Chuck Moore
Moore Bettah Ukuleles
http://www.moorebettahukes.com

Check your action at the first fret,it should be about 1mm.
If it is much higher,then this might be part of the problem.