Camera Recommendations?

As I was sorting through pictures for Joel's baby dedication, I became more and more disappointed. While we were in the hospital I had some trouble with my camera. For some reason all the pictures were coming out dark and blurry and we had to retake them several times. Consequently, we don't have a lot of really good pictures from those first moments. I hadn't thought much about it until I started going through the pictures again. A lot of them are really bad. It is kind of heartbreaking. This is the only picture I have of my dad holding Joel in the hospital because my camera was acting up. That is a moment we'll never get back. Many of the pictures taken since then are not so great. The only times I seem to get really good pictures are when conditions are absolutely perfect (outside with no flash--not really an option in February).

I am very dissatisfied with my camera and on the hunt for a good one. We have some Christmas bonus money left over and will probably have to save up more, but we've decided it is an investment we are going to have to make. The one thing I do like about my camera is that it is small and portable. I can stick it in the diaper bag or my purse and always have it with me for those unexpected moments.

Some features I would like are:

• Small
• Rechargeable battery
• Higher megapixle (so you can zoom in on part of the photo and blow it up without the resolution being too low)
• Good zoom
• A point and shoot option (so I don't have to mess with the focus unless I want to)

Any advice would be greatly appreciated.