The first thing you should do is take a good close look at the lens and look for a fingerprint or smudge on the lens.

Next you need to look at the EXIF information that is embedded in every digital photo.

If you don't have software for reading the EXIF information:
Right click on one of the photo files that looks like you described.
Then click the Summary Tab.
Then click the Advanced Button.

Let us know what you read for:
Shutter Speed
Lens Aperture
ISO speed

We can better provide an answer if we have that information.