I can tell that you're very frustrated.
But if you're explaining the problem to them like you are explaining it here, it's no wonder neither the hosting company nor your ISP understand the problem. You need to trade a little of the heat for some light.
Because of spam, few companies are willing to risk open relays. You can set your email program up to use a POP3 mailbox at Dreamhost, or a POP3 mailbox at your ISP; it doesn't matter. And if you use something like the highly powerful and highly versatile Pegasus, you can even pick up your email at a bunch of different POP3 mailboxes all with one click of the mouse.
But you probably need to use your local ISP for SMTP (outgoing) mail.
The fact that your POP (point of presence) phone number has changed is immaterial. And most of us get a different IP number every time we dial up our ISP. The fact that your access number and IP changed shouldn't make a bit of difference at all.
Just set up your email program to use the name of your ISP's SMTP server for outgoing mail and you should be OK. (Since you refer to your ISP, I assume you have an ISP, rather than an OLS like AOL, which does not offer an SMTP server.)
Alternatively, you can use squirrelmail, and read you mail with your browser. If your domain is www.jr_chicago.com, you would go to http://webmail.jr_chicago.com and enter your username and password to access mail in your Dreamhost POP3 mailboxes.
If this doesn't solve your problem, then perhaps you could calmly and quietly provide enough detail so that others could understand what your problem is.