Why does my MacBook Air's screen look odd for about 20-30 seconds after the battery burned out and I turn it back on?
Normally when you put the Mac book to sleep, it powers down the CPU but leaves power supplied to the memory and other internals so that when you wake it up it can start right away. When you run out of battery power, though, it has to write all of the memory to disk because it doesn't have enough power left to keep the data in memory.   This is called "hibernating" or safe sleep.

When you wake up from hibernation, it takes some time (typically 20-30 seconds) to restore the data from disk to memory. I think that's what's going on in your case.  Is the computer responsive when the screen looks odd like this? If not, then that's almost certainly what's going on.