First thought: failing internal drive.
Any way you could try booting from an external drive?
You could boot from recovery (press alt at startup) use Disk Utilities to clone your internal to an external, and if the external boots fine, continue to boot from it until you can get the internal replaced.
Does booting in safe mode help? (Press shift at startup)
If it's only a problem with the boot time and it works like it should after a while, you could simply stop shutting it down, and just set the display to sleep after a period of inactivity. I keep my mac running 24/7.
But you should seriously diagnose that drive the best you can. Start with Disk Utilities.
What kind of drive is it? The original 'Fusion Drive'?
Anyway, you should back up that disk, if it's not already backed up.