iTunes would be the obvious one. Why you could listen to pandora but not iTunes I can’t imagine, so try that first I’d say. You could always create a second account for use at work, using say your work email address.
I’ve tested it on Chrome, Firefox, and Safari on my Mac and on my iPad. I make no promises for Windows, IE, or Android; but I don’t know of any reason why it shouldn’t work for those as well.
The only podcasts I’ve found that won’t work with it so far are Escape Pod (mentioned by Mama Zappa below) and its sister podcast, Podcastle. I don’t know why those don’t work so I probably won’t be able to fix them. If you find other problems, please let me know.
I apologize for the way it looks, but no one’s ever accused me of being a designer!