It happens quite often that I cannot activate the Scavenger Trinket after having used and it has cooled down. I have no idea why as the icon shows it to be completely cooled down but when I select it and click like mad, nothing happens for a long time. If I switch to my weapon, kill some orks and wait some time it will work again.
While the scavenger trinket is active, your character will have a blue-glow, and get an extra 1 gold every time you (or one of your traps) kill a unit.
The amount you earn for a kill is always shown breifly as a number displayed over the orc when you kill it; this number will go up by 1 when the scavenger trinket is active.
See also this question for information on how the ability stacks in coop.
The issues you are having are probably due to the trinket being on cooldown (shown in your inventory as being partially grayed-out), or not having enough mana to cast it (the blue bar at the upper-left of your screen).