To clarify, when you say "opens up btinternet " is this a dial-up/connection window or some other programme or are you referring to the BTI home page that appears in Internet Explorer when it opens ?
If it is not the page appearing in IE try again what BombayDuck proposed and use the following amplified procedure from Microsoft.
The key will be to start IE from the Start Menu or desktop shortcut right after you check the "IE should check to see whether it is the default browser check box". Then when the default browser prompt appears:
1. Un-check the Always perform this check when starting up check box
2. Click Yes to make it the default browser
MORE INFORMATION
To configure Internet Explorer as your default Web browser, start Internet Explorer, and then click Yes when the following message is displayed:
Internet Explorer is not currently your default browser. Would you like to make it your default browser?
If you do not want Internet Explorer to be the default browser, click No. To prevent this message from being displayed again, click to clear the Always perform this check when starting up check box before you click No.
By default, Internet Explorer verifies if it is the default browser each time it starts. If Internet document (HTML) files are associated with a different browser when Internet Explorer starts, Internet Explorer recognizes that it is not the default browser and prompts you to make it the default browser.
If your earlier version of Internet Explorer had not been configured as the default browser, Internet Explorer is not automatically configured as the default browser and the preceding message is displayed. If you do not enable Internet Explorer to configure itself as the default browser, the message is displayed each time you start Internet Explorer until you click to clear the Always perform this check when starting up check box.
To manually configure Internet Explorer as the default browser, use the steps in one of the following sections, depending upon your version of Internet Explorer.
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Internet Explorer 2.x
1. Start Internet Explorer. On the View menu, click Options.
2. Click the Advanced tab and click to select the On startup, perform check for default browser check box.
3. Click OK.
4. Quit and re-start Internet Explorer. Then when you are prompted to make it the default browser, click Yes.
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Internet Explorer 3.x, 4.x, 5.x
1. Open Control Panel and double-click Internet Options.
2. Click the Programs tab.
3. Click to select the Internet Explorer should check to see whether it is the default browser check box.
4. Click OK.
5. Start Internet Explorer and when you are prompted to make it the default browser, click Yes.