It would depend on the type of computer case you have. If it is a Dell or Gateway or Hewlitt packard style case, you may have difficulties. One of your computer savvy friends can probably tell you. Worst case scenario (pun intended) you can get a completely new case anywhere between $60-200 depending on features, space, etc.
As to whether a motherboard replacement is viable, it really depends on the state of the rest of the components in the case. If you have a fairly good video card, SATA hard drives and a SATA optical drive then rebuilding would likely be the lower cost option. You will likely have to replace at a minimum, the motherboard ($150-ish), processor ($200 on up depending on features) and Ram ($60 for 4GB DDR2, more if you go with a board that takes the newer DDR3). if your video card is older than a year or so, getting a good card like a 9800 gtx+ will run you $160. If you intend to reuse any of the old components you will want to test them before you purchase anything in a different computer.
Also, chances are that even if the power supply works still, it may have had a hand in the failure of whatever other component is actually failed. I'd reccommend replacing it with a 650 watt power supply. Antec makes a decent one that usually runs about $80.
If you decided to scrap the oritional drives too, a decent 300gb SATA hard drive costs about $70, and a 22 speed DVD burner costs $30.
as to the complexity, there are a few steps to building a new computer, and there are ways that you can accidentally damage components, but only if you don't follow instructions and are not paying attention. If you know someone who has built a computer before, I'd suggest buying them dinner in return for them showing you how to build your first one or something. A storebought computer will be cheaper, but you will not be able to upgrade it nearly as long as one you build yourself, and if you are building a high powered gaming rig, you will be able to build it yourself far cheaper than what the major companies would charge you in the long run. The downside to a build it yourself is the warrenty options, since every component has a different warrenty, keeping track can be a pain.
I think knowing how to build a computer is an excellent skill to have, but you really have to ask yourself if you want to put in the effort to learn how, or are you willing to spend $200 more for someone else to do it for you.