That inductor seems to be part of an LC output filter. Typical values are roughly around 10µH, but the exact value isn't critical. The maximum current is more important. Measure the diameter of the inductor's enamel wire with a caliper to figure out the current rating. Presumably the inductor got hot because of the bad filter caps, e.g. high current draw. And even with the toasty appearance it could be still fine. If the monitor runs great with the new caps simply keep the inductor.