Lots of good advice here Mr Beefy, and some that doesn't apply as your 2800 is fully automatic with no manual settings for shutter & aperture. But something's not right. With that camera you should get better results. But you dont tell us what lighting situations give blurry pics without flash.
Is it indoors or outdoors? Without flash, you cant expect most cameras to produce good sharp well exposed pics indoors, where the lighting is inadequate, photographically speaking.
I'd agree with Kev61. I had the 2800 before getting my present Fuji602. Love them both and look back at the great 2800 pics.
What to do? Maybe some camera like Kev mentions with higher ISO 800 would help, if you really need to take pics without flash in dull interiors.