Why desktops are preferable to laptops or all-in-one's from a repair perspective.
Desktop hardware repair can be relatively easy, as components are easier to get at and replace. Parts are generally non-custom (with the exception of some name-brand small-form-factor computers from the likes of Dell and HP) and so are easy to find replacements for. Most of the time the problematic components are just the storage drive or memory. But sometimes there can be an issue with parts or cables coming loose, particularly after the computer being transported, say, to a new home.
Being certain of whether a problem is hardware or software-related is not an entirely easy matter, but it pays to check the hardware anyway in most cases (old hard drives in particular have a limited lifespan), but generally-speaking if you're experiencing random restarts or the machine turning off without properly shutting down, it's probably a hardware issue (there are some exceptions).
One of the main reasons I recommend desktops over laptops for the bulk of people is that the parts are so cheap. A replacement power supply can be only $75, and takes only a short period of time to replace. If you need an assessment of your existing machine, feel free to give me a call and we can discuss options. Dropping it into the workshop may be possible and will result in a lesser charge than if I have to come on-site.