Chosen Solution

Received 2011 Apple iMac from an estate sale. Turning power on, it boots to login screen but have no way to get past it. Bluetooth keyboard, mouse and trackpad all seem to be functional, but are not recognized by computer. Plugging in a USB keyboard also does not work. It is also password protected which I do not have either. It’s possible it may have been hit with a power surge at some point. Any ideas on what I can do?

There are two kinds of access here. The first is the system firmware lock which looks like this:

Here you’ll need to get the original grey disks the system came with as you’ll need to boot up under the diagnostic disk to gain access to the utility it has to reset the password. If you are lucky and the system had a newer macOS installed then it might have a recovery partition present, then you can boot up under it to get to the utility Forgot a Mac Firmware Password? Don’t Panic, Here’s What To Do The user Login screen which looks like this:

Here you only need to reformat the drive using an external bootable macOS drive and then re-installing the macOS (Sierra being the highest I would go with) In both cases you really need to use a real Apple USB keyboard and mouse.