You don't want to use a vacuum cleaner because a typical vacuum cleaner is belt-driven and can give off static discharge. In a repair shop you would use a direct-drive vacuum cleaner with ESD-safe plastic nozzles but at the same time I would never think to use a vacuum cleaner on a laptop.
In all honesty once a laptop is dead like this I've only rarely seen them come back to life without a system board replacement. And a system board replacement out of warranty never makes sense unless you hunt ebay for weeks and get lucky.
If it were my laptop and I had given up hope of warranty replacement, I would strip it down. I would remove all the drives, the wireless card, any other removeable cards. I would try to re-seat the CPU if it is a socketed one. Only once have I seen the resocketing fix a dead laptop, however. I would make sure the CPU fan is not blocked or somehow not spinning because perhaps it is not and the computer can sense this. If there are more than two leads coming to the fan then it probably does have this ability and is therefore refusing to turn on. Doubtful after only a year or two.
I would also re-seat all connectors internally and try running the laptop with just the system board, CPU, RAM, and LCD. Look at all the external connectors and see if any pins are bent against the ground shield. Also, try removing the CMOS battery if it has one and leave it out for a few minutes and reinsert it. Again, only once have I actually seen each of these ideas fix anything. It's probably a dead system board.
If you have never taken a laptop apart before, I'll tell you the most fool-proof way: Take several sheets of blank paper and draw small diagrams of each stage. Then, as you remove each screw lay them next to the diagram, next to like ones. After this, draw arrows going from each pile to their spots. Tape them down with scotch tape. Then, move onto the next step and draw another diagram. I start at the bottom of the notebook, move onto the top, remove the keyboard, unscrew LCD hinges and connectors, remove LCD, remove any bezels and CPU heatshields, move onto various connectors and system board screws, and voila at that point system board is out. Been using my paper/tape method since 1997 in various shops and it has never failed me.
edit to add:
Also forgot to suggest two more ideas: Try connecting a VGA monitor and see if anything shows on it. Also try checking the voltage coming from the DC adapter. It is admittedly extremely rare to see them fail.