The 7812 is ion a substantial heatsink with a number of other devices, it is possible that (since they are all electrically insulated from the heatsink) that one or more of the insulating bushes has failed and that there is a short through the heatsink. Before you disconnect anything from the heatsink, see if there is any continuity between the tab of the devices and the bolt that fixes them to the heatsink and/or to the heatsink itself (normally the bolts are in fairly good electrical contact with the heatsink). This is not very likely, but well worth checking. If, when you do remove the device from the heatsink, you find any of the plastic parts are damaged, cracked, or have metal shards on or near them, replace them!
Oh, and if any of the bolts seem loose, they may have shaken loose or they may have stripped threads -- replace them and use shakeproof washers and/or locktite (etc) and DO NOT over-tighten them.
But back to our regular scheduled program...
12V regulators are cheap and should be fairly well protected against overload.
You don't mention that it is hot, so I will assume that it's not, and that means it hasn't shut down due to overload, and nor is is shorted out.
Given that, I'd replace it. It may not fix the problem, but it might help diagnose it.
If the problem is caused by a shorted output, the device will last long enough to get hot, and probably go through several (probably indeterminately many) shutdown cycles before it finally expires. However if this had been happening I think you would have seen symptoms different to "it suddenly not powering up one day"
