I live in Greece and have bought an n810 a few months ago from the USA. Now the tablet doesn't start up at all, and the local Nokia office says it's out of guarantee because it wasn't bought from the EU (although it's only a few months old).

Any advices to have it fixed somehow, besides paying the local office?

That's one of the risks of buying the tablet in the states: nokia won't honour the warrany.
But since you can buy almost two tablet for less than the price of an european one,it kinda offsets the risk.
Pity you were unlucky and got a failing device.
Are you sure it isn't the battery and/or the charger? That would be relatively cheap to replace.

Does it not power up at all, or does it "just" fail to boot? In the latter case you may be able to fix it by reflashing, otherwise try testing the battery in another compatible device (for example E61i or E90).

It may also be that it originally failed to boot even to the battery charging runlevel, but that the battery has now been drained completely so it won't power up. You can try charging the battery fully in another device and then trying to flash the N810 with it. IIRC the bootloader will refuse to flash the device if the battery charge is less than 50% or so.

Sorry, I have no idea how to get nokia.gr to behave reasonably :-(