Unfortunately, because it's integrated with your modem, responsibility for it falls squarely on your ISP. Quite frankly, referring you back to Apple support is a cop-out on their part, probably because they lack experience with Macs.
I can give you a few general things to check, but in the end, if you're typing that password correctly and are using a modern form of encryption, it should be working. If it's not, you're probably going to want to look into getting a more mainstream wireless router.
Things to check:
1. Ensure SSID broadcast is enabled.
2. Make sure WPA/Personal is set as the wireless security type (if you can't get into it with security turned off, this won't help).
3. Scan for other wireless networks in your area using a tool like
AirPort Radar. If there are others, make sure you set your channel to something other than what the others are using (I typically suggest a lower number like 3 or 5).
4. Do a cold reset on the router (this is typically done by starting with the power cable unplugged, press and hold the reset button on the back and continue holding for 30 seconds after plugging in the power).