Are you sure it wasn't in a wet or very humid place? In my (limited) experience liquid damage is the most common reason they don't power on or charge. While it's true there is a fuse that could blow that would also cause it not to power on, it doesn't just blow for no reason. I've only found blown fuses in 3DSes that had already had botched repair jobs done on them. It's not something that would happen just from leaving the console unused for a while.
If you're willing to open it up you can't really do any harm by cleaning it with high concentration isopropyl alcohol. Just use a clean toothbrush and be gentle disconnecting all the ribbon cables. The worst that can happen is that it still won't work. The alcohol won't damage anything as long as you let it dry fully before you try powering it on. Just be sure not to let any migrate into the lower LCD, since it could leave marks on the backlight. Optionally, you could first remove the motherboard from the housing to be absolutely certain you don't damage the LCDs with alcohol.
I just posted this in another thread, but it seems relevant here: you sometimes find corrosion under this metal shield beneath the WiFi board. You can clean beneath without desoldering it if you have a toothbrush with some flexible bristles that can reach that far.
