Never, ever use the blowing end of the vacuum cleaner (Hoover) to blow out your case!! A technician where I worked told me that tip. Use canned compressed air for that.
If you are still having problems after cleaning and satisfy yourself that the cooling is OK, then it is time to move on to the PSU. Since you mention that you know of a shop, bring it to them and tell them that you suspect the PSU as being the culprit. If you need a new PSU get one that is rated higher than the one you currently have, that way if you end up upgrading something you wont have to worry about enough power for the new hardware.
If you do it sooner than later you will have time to insure that they fixed it correctly before your off to school.
Good luck with the computer and your studies.