Monitor not detected after trying with several cables

I looked at the description of the monitor. It said that the monitor had VGA, DVI-D, and DisplayPort inputs. The monitor does not have a HDMI input.

Given this, why are you using VGA and HDMI adapters instead of a Mini DisplayPort to DisplayPort cable?

The resolution of the monitor (1920x1200) is such that you could use a mDP to single-link DVI adapter, but why bother?

First I would test the Dell monitor that you purchased from e-bay with another computer to make sure that it actually works.

FWIW Apple made some Mini DisplayPort to DVI and VGA adapter back in the day, but they had a pretty high failure rate.

For example > https://www.ebay.com/itm/204212701142?

Personally I do not purchase from e-bay.

If the Dell monitor is working,

maybe try the > https://eshop.macsales.com/item/Apple/MB570ZA/?

or the > https://www.amazon.com/DisplayPort-Thunderbolt-Compatible-ThinkPad-SurfacePro/dp/B0796C2QC8/ref=sr_1_2_sspa?

The 2011 iMac has Mini DisplayPort output and requires a Mini DisplayPort adapter.

That Dell monitor has HDMI, DVI and VGA inputs.

Use a Mini DisplayPort to HDMI adapter and HDMI cable.

https://www.amazon.com/dp/B07JDWR6W9/ref=sspa_dk_detail_1?

Or a Mini DisplayPort to DVI adapter and a DVI cable.

https://www.amazon.com/DisplayPort-Thunderbolt-Compatible-ThinkPad-SurfacePro/dp/B0796C2QC8/ref=sr_1_2_sspa?

Or a Mini DisplayPort to VGA adapter and VGA cable.

https://www.amazon.com/DisplayPort-Benfei-Thunderbolt-Compatible-SurfacePro/dp/B0795NH9Z2/ref=sr_1_1_sspa?

The Benfei adapters above are purely for example.

Personally I would go with a Mini DisplayPort to DVI adapter and a DVI cable.

Good catch Servant of Cats.

It does look like that Dell only has DisplayPort, DVI and VGA connections.

It does sound like some sort of hardware failure... a bad port, maybe?

Exactly which adapter are you connecting to the iMac?

Have you successfully used any other monitor recently with it?