Some airlines allow a lot more pieces of checked luggage than others. While this depends on the origin and destination, you can sometimes go as far as up as 10 (!) pieces, see [this question of mine][1] from when I moved to the Netherlands. I brought a single desktop computer which I stored inside the box its case had come in, with the Styrofoam padding, and with space for the mouse, keyboard and some more stuff. It made the journey fine (although I did have all the data backed up just in case). I also dis-assembled and bubble-wrapped a monitor - but that wasn't a piece of checked luggage in itself; and I'd be more worried about those.

You can have a look at some Dutch (online) stores for prices of monitors and other parts to see if the hassle, the transport costs and the risks are worth it: [Alternate][2], [AFuture][3] and others; [Tweakers.Net][4] has a [price comparison mechanism][5]; and of course there's [Marktplaats][6] for second-hand items. 


  [1]: https://travel.stackexchange.com/q/53706/33321
  [2]: http://alternate.nl/
  [3]: http://afuture.nl/
  [4]: https://tweakers.net/
  [5]: https://tweakers.net/pricewatch/
  [6]: http://marktplaats.nl/