Thats right, the live you put to the battery you should have removed from the relay to be able to do so? The terminal opposite should have +12V best to have ignition on at same time in case fans are under igntion control on these. If you don't have meter you can easily tell by connecting the wire you have previously to the battery to this wire. At which point the fan should run. If not this means you don't have power at the relay.

I still think it will be a power problem or wiring problem as the relays and switches are reliable, the relays are prone to sticking sometimes which is easily solved with a slight "Flick" or tap on the casing which frees the contacts but when the happens the contacts usually jam closed hence you have the opposite problem with fan on all the time.

Martin