If it is anything like most older stoves with that sort of outlet, someone has plugged in something that draws too much current, and shot the fuse. Somewhere in the stove will be a regular screw in 15 amp fuse, just like the ones used in the fuse box of an older home. I've seen lots of stoves where people said the outlet didn't work, and even if the fuse didn't look blown, a new one fixed it right up.
Actually, from what I understand (I don't have one of these), the griddle receptacle is only for control, as the heat comes from the Calrod surface units below. When the griddle is plugged in to this, it connects the two units it sits over to the griddle control. I don't think the griddle itself has any heating unit in it. Someone please verify this.
I have this exact '58 Liberator in Sunshine Yellow
and yes the griddle heat is provided by the CalRods. Mine is missing the Griddle and Meat probe though, wish we had them! This one on eBay doesn't have the 2nd smaller oven it seems, just the storage unit.
The griddle "plug in" is merely a switch that ties the left 6" and 8" elements to the control for the temp-controlled front burner and it's slide control on the panel (far left). If the Sensi-Temp unit isn't working, it can be replaced with an infinite heat switch and if wired correctly, the switch will still work for the griddle. Mine was and does
Love that stainless door on the side storage sections, mine didn't have them (option when new).
This one only has 2 rotary knobs since it lacks the small oven. WE'vve found that we use the smaller oven about 80% of the time, we'd hate to do without it now!