Lenovo G580 stuck on boot screen.

One possibility: Sounds like hard drive boot sector corruption. Run the system recovery tool by booting the Win 7 DVD and tell it to repair the boot sector.

When asking for password have you tried just hitting the "enter" key, or typing in "password" and hitting the "enter" key?

If this fails, Windows 7 may be installed in protected section on the hard-drive. Pressing the correct function key on start-up may get you to the point the computer can reformat and re-install Windows 7 to the point the computer was brand new.

This works if Windows 7 came installed on your computer. Read the information that came with your computer for the correct reset procedure and Function key that works for your model. I needed to do this on my Asus gamming laptop (circa 2010) when Microsoft Windows 10 tried to download at the same time Windows 7 updates were downloading.

If you Google your computer's brand & model you can find the information for re-setting you specific computer model on the internet.

Had similar issue with my Toshiba. Shut it down, unplugged it, removed battery and held off button for 15-20 seconds. Reinstalled battery, plugged in and turned on.

If I try to boot with a Windows 7 install disc I get the following error:

Secure Boot
Image failed to verify with ACCESS DENIED

I'm positive the issue is the bios reset itself to some defaults with the secure boot mode on. Only way to clear it is from within the bios. But the bios set some sort of default password (I never entered any). Removing the cmos battery doesn't clear the issue nor the password request.

I think the Bios password is NOT your not login password (that you have never set)
It is something different
On the web, you can download an ISO file called the "Ultimate Boot CD"
http://www.majorgeeks.com/files/details/ultimate_boot_cd_(ubcd).html
This might help you get it booted,