Sony HandyCam HDR-SR10E ... help :(

[softball]

try it outside in the shade with your colour balance set to the little cloud and report back.
When you shoot inside, you should be using lighting in most conditions and the colour balance should be set to the little light bulb.
Another thing you should try is kicking up the gain. Look into your manual as to how to do this. In fact read your manual from cover to cover to get an idea of what you are doing.
This is a thousand dollar camera and I suspect at that price, its low light capabilities are sketchy.
Its all about lighting.