*Is installing a new PSU a job a non-expert can do?*
Yes it's very easy - basically a few screws and a number of plugs
You will have to get an equivalent sized PSU - which is not the same as a "standard" one from a regular tower.
This is a Shuttle PSU click here but you should check with them first to see if it's a direct replacement for your particular one.
One word of warning - PSUs that go pop can sometimes damage other components, including the motherboard, plug-in cards - and hard drives. Not always but sometimes9.
If you have access to a spare regular PSU you can use it carefully without fitting it to the case, and check if anything else has gone. If other parts have blown too, your best course of action may be to replace the whole she-bang.
If it was during a Thunderstorm, check your insurances.