Yup, and I'm surprised that your particular processor doesn't support SSE2. But, as you know, it doesn't.
The bad news is that your particular processor has a socket A attachment to the motherboard, and there seems to be no processors with socket A attachments that have SSE2 support. If I'm right (I think I am...), this means you'll need a whole new motherboard too.
But, do you really need Elements on? You can get a lot of other software that will do your photo editing for you, that probably doesn't need SSE2 support. Photoshop CS itself, for example, can't need it, because my Dad has it installed on our old Athlon 1.2GHz computer, with an older processor than yours.
My suggestion would be to try Picasa:
http://picasa.google.com/