Having access to www.roadrunner.com (as anyone does) doesn't change your connection speed through your ISP (Verizon). In effect, Roadrunner does not become your ISP simply because you can access their webpage. A web browser is just a means to access content through your existing ISP, so changing to a different browser won't do it either. If the browser itself is causing issues, you could always install a different browser such as Chrome or Firefox.
If you want faster internet at your business, you can check with Time-Warner (or other ISP) to see if they can provide service at your location.
I am using a Verizon Wireless modem for high-speed internet at my business. I have TimeWarner cable internet with Roadrunner at home and it blows the doors off the wireless modem. I am also using Outlook with my verizon modem, having been force-migrated from Hotmail. I can bring up Roadrunner in Internet Explorer by simply typing www.roadrunner.com. I wonder if I can actually use roadrunner as a browser on my verizon wireless account, without being a subscriber to TimeWarner cable. Does anybody know if this will work? Can I replace Internet Explorer with Roadrunner?