The memory stick is not the issue. The memory stick will either work, or it wont work, but it has no effect on the image processing or exposure. Its also very unlikely to be the battery (theoretically possible, but highly unlikely, likelihood raised if you bought a cheap generic battery from hong kong, but even then still unlikely).

It is possible that you have adjusted the wrong settings in your camera (even though its on "auto", many manual controls can still be enabled) For example, your metering mode, if set to something more geared for manual controls like "spot" or "center weighted", certain tones and brightness values can trick the meter into an incorrect exposure, you need to use them a certain way or they will only ruin the cameras exposure reading. If this is the case, simply switch back to evaluative.

Another thing is the ISO might be set and stuck at something really high like 3200, in which case, the images would likely wash out or overexpose in bright sunlight, with a shutter that can't properly expose a bright scene for a 3200 ISO. This could explain the "pixelation" you mention.

The blurriness doesn't seem to collaborate with either of those explanations. it could also be a combination of issues and adjusted settings, another possibility is exposure compensation, which could slow the shutter down, increase iso, wash out and blur stuff etc.

Anyway, hard saying for sure, if you post up an example of a bad pic, we can likely look at and be able to identify exactly what went wrong with the exposure. If its a problem with the cameras sensor, that would be identifiable as well.

Finally, another issue with your zooming in might be caused by lacking light. The cameras lens is built to find focus much faster at wide angle than telephoto, at telephoto the lens lets in less light, and must find a much finer detailed contrast.

Hope that helps, welcome to the forums!