does it also say you're not connected to the internet? does it try to find the page for a long time or does it give you that message straight away? you can tell if you're connected to a network from the stripy upside down triangle in the top right corner next to the volume, clock and charge icons, if any of the lines are black then you are connected to a network. if the triangle is solid white then airport is turned off and then you click on the icon to turn it on again but it doesn't sound like it's off, it sounds more like a configuration issue. easiest way to fix it is usually to turn everything off for about a minute and then back on again, works more often than you might think.
eta: bluetooth shouldn't make a difference in this case, it's really only used to connect to things like phones and other peripherals that use it (for example the apple wireless keyboards and mice), but for internet it's not really important. you might actually want to keep it switched off if you're working off the battery, it can be a bit of a drain.