You can go to any other working page on your site, switch to design tab and uncheck web part content check box, like this. This way if the web part code is written correctly - it is not supposed to render any content in design mode. Now you can go to your page with error and safely remove the web part from the template or disable it.
Most likely you have a sql call which timing out.It probably takes more than 90 seconds to execute your call. Do you use any update panels for your web part on your page?
You might add to your web.config
<httpRuntime executionTimeout = "number(in seconds)"/> to see if that solves the issue.(topic on stackoverflow), but I believe that you need identify the problematic SQL query and fix it.