Why unstable & what damage will it cause?
I have my computer all setup for awhile. I am oc'd from 2.4ghz to 3.4ghz. When running Prime95 one core passes the stability test over a period of 8 hours while the other fails after 8 minutes. The timings are 4-4-3-8 @ 2.2volts and is rated at 400mhz. The fsb at the moment is only 378mhz. The vcore is @ 1.4125 and mch on auto. Why is the one core unstable while the other is stable and will it hurt anything to continue to run it like this? I notice no problems in windows, etc for now but don't know what could happen long term. How can I make both cores stable as well, is it normal for 1 to fail soon while the other passes?
Yes, it is normal for one core to fail, doesn't really mean a thing except that you are not stable. I doubt that you will hurt anything if you run as is but you really don't want an unstable computer - you could loose data or have corrupt files.
I assume from what you say that you have an E6600. It should easily handle 3.4 and your vCore should be high enough. Your memory timings are probably too tight. Try relaxing them to something like 5,5,5,15. It that is stable you can then gradually tighten until your system becomes unstable and then back off.
You don't mention temps or type of cooling. You certainly shouldn't be oc'ing to 3.4 with a stock cooler.
If that is the case then your memory should be fine and you probably got a CPU that doesn't OC quite as well as some others. You may need to back off the OC a little to get stable again. As genec57 said you probaby wont hurt any of your harware by running at unstable speeds but you could corrupt (and loose all data on) your HDD or you could have errors running programs (resulting in mysterious crashes) especially when you are pusshing the machine hard (doing something you don't want to interupt).