Enda O'Coineen did it in 1985, Arek Pawelek (who posts on RIBnet and is currently going round Cape Horn in a RIB) did it in 1998. As far as I remember they mostly sailed/drifted across.
Alan Priddy and his team first did the Atlantic in 1997, and have done it a few and a bit times since. Bear Grylls and his team did it in 2003. Arnt Remy Åvik is planning a solo attempt from Norway sometime this year or next. Search here for Grylls and you'll find all sorts of discussions about Atlantic crossings, and who did what when. Probably best to make a cup of tea first, because you'll be reading for a while!
As far as I know, there hasn't been a non-stop crossing in a powered RIB. The power/weight/speed calculation just doesn't add up for that sort of range.
Are Parker planning something we ought to know about?