Your site looks like a big pile of Flash.
Flash exploits are everywhere, all day long.
Flash is a no-no. No Flash. None.
Flash bad. Beer good.
I looked at your source, and the offending code is here:
Likely someone has tacked it onto your page with an off-the-shelf script kiddie program.
As for the insertion vector, without shell access I really can't tell you how they got in.
You should edit your html by hand (step slowly AWAY from the Dreamweaver) and remove the offending code.
Of course until you secure the site, it may be infected again shortly.
From your WHOIS info I can't tell who owns your IP.
Are you on bargain shared hosting, VPS, dedicated?