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The main problem I've had with building my own PC is that it can be a pain to work out what component is causing problems if the system is unstable.
I've built two PCs and both times at least one component had to be sent back. A bad hard disk was easy to diagnose, but the faulty motherboard and RAM I recieved both caused very similar stability problems. I had to borrow spare components to isolate the faults, I don't know how I would have found them if that hadn't been possible.
Obviously if the computers had been bought ready built these problems would almost certainly have been found in testing. If a fault did occur I could have just sent the whole machine back rather than having to find the faulty component.
I've also heard a lot of horror stories about PC mail order companies refusing to replace faulty components if they suspect that they were damaged during installation. I know swome places that will hardly ever replace CPUs, as they assume that they must have been broken during installation.
Personally I would never build a PC again after my bad experiences. You don't save any money, you can get PCs custom built to your spec for the same price as buying all the components. Unless you're looking for a hobby and you're not too worried about wasting money or actually having a PC that works, I wouldn't recommend building your own PC.