RAM can definitely cause random shutdowns but being that the computer is only 4 years old, it doesn't seem likely but it is very possible.
PSU overheating can occur but I seriously doubt within 5-10 minutes of booting.
You can actually get her to check the fans, just have her hold her hand in behind the PSU fan and see if warm air is blowing out at a decent rate (she should feel it gently, not real hard but not very weak.) Often manufacturer computers don't have much in the way of cooling, often a CPU fan and PSU fan are the only things in there so it is possible but it takes a while for a computer to overheat.
I would recommend a new surge protector (not to be confused with a normal power strip). The light is usually a "ground light" and if it is flickering then the ground wire could be faulty and have a bad connection.
Dust is usually a minor problem, it can cause more heat but often problems with a computer are the result of a more serious problem than just dust.
Depending on your familiarity with her (co-worker you hardly know, acquaintance, friend, etc...) you could either ask her to bring it to work so you can look at it (during break hours of course) or if you are a friend, possibly making a house visit (this might be kind of weird but it may be the easiest way to fix it if she lives close by). Do this only if solving it over the phone doesn't work. If the PSU is fine and a new surge protector doesn't fix it, RAM is the most likely culprit for things like this.
