With computers getting them clean-room clean is usually a waste of time and money. It is also potentially hazardous. In an hour of run time they are going to show some dust anyway. Go for a solid 85% or 95% clean and call it good enough. I've seen people damage circuit boards worrying the last specks of dust out with compressed air, brushes and swabs.

Cleaning more frequently to a lower standard is better than getting it 'really clean' once every decade. The $5 cans of air work fine but you still need to practice restraint. You can use a brush but gently, gently. Being a barbarian, and heretic, I use an industrial air compressor at 120 psi and keep the nozzle about a foot away. Good advice on restraining the fans from Compugeek.

Yes, if you do it inside you're just shifting the dust around. No big deal if the PC isn't too dirty. Next time you vacuum and dust you get most of it. If the PC is really dirty blow the dust out outside or arrange a fan to blow the dust out.

If after you clean the PC it beeps at you or fails to start first time open it up and examine it carefully. Don't just keep restarting it. Check very carefully to make sure the heatsink/s are seated properly, that all the fans are still connected and running. That the memory, cards, and all connectors are seated firmly. Look for foreign objects that might cause a short and if the mounting spacer might have collapsed or fallen out allowing the MB to short out against the back plate.

PCs have come a long way in protecting themselves. I caught a motherboard with a paperclip that got picked up during cleaning and caused a short. That sort of issue used to be the death of a board. This time the start-up pre-test caught the short and shut the process down before any damage was done. The guy would hit start and the lights and fans would start and then it would beep a couple times and turn off. Good thing he brought it to the shop after just a couple of tries. I remove the paperclip and it ran like a champ.

A heatsink that gets banged loose is another common fault. The CPU overheats after a few seconds and shuts the PC down to protect itself. Keep trying and eventually the CPU fails. Reseat the heatsink and all is well. Some CPU/motherboard combinations are self protecting. More and more are these days. But a few don't. It is a feature worth having.

They don't always protect themselves but PCs have got a lot tougher over time.