It appears that several of my domains ended up with infected pages. I do not know how that happened and neither does Dreamhost. This is currently my second fresh install. What a pain in the buttocks this was.
Hopefully, this will be the last time! I changed my password for the second time, plus I added an additional FTP user to separate the most important sites in an effort to contain any future infections.
EDIT: On a positive note, I updated WordPress and it appears to be working well.
Infected websites suck!