Restored from Time Machine, no boot
A restore of Time Machine back to the drive will not restore it to a bootable state. You must install the OS onto the drive from the install download (Lion) or install disk (pre-Lion).

To do what you expected you need to make a clone of your boot drive. Use a tool like Carbon Copy Cloner. It makes an exact copy of your drive. If that drive happens to be your boot drive, then the clone is bootable.

Time Machine is great for recovering lost or earlier versions of your documents/data; Carbon Copy Cloner is great for keeping a current snapshot of your entire hard drive that is bootable. Use Both; I do.