airport extreme with attached usb drive works for time machine
That's an option, but it's not technically supported by Apple (go figure).
However, you can also attach the external Time Machine drive to your desktop and have your MacBook back up to that Time Machine drive (a long with your desktop). That's what I do with my MacBook Air. It works great and since my Mac mini is always turned on, it's fine.
If your desktop and MacBook both support Wake On LAN (via wired or wireless) and you own a supported router, the MacBook will wake up the desktop and Time Machine drive from sleep.
Good luck. Once you get Time Machine going, it's great. I even removed the icon from my menu bar so I just forget about it. However, like you, I had nothing but problems with the Time Capsule. Personally I feel it's one of the worst products to come out of Apple in a long time.
The enclosed, non-removable hard drive is a disaster waiting to happen. I expect we'll get new smaller revisions to the AirPort Extreme soon. I wish they would just officially support Time Machine over an AirDisk drive (like Jobs originally announced way back in 2007) and kill Time Capsule all together. Or at least make it user-replaceable (could be similar to the bottom of the new Mac mini.).