Hi Niek, and welcome to the forums. Unfortunately, Chumby as a company no longer exists -- hence why you're not getting any response from their support. Your best bet would be to find someone (possibly on eBay or the like) who has a Chumby One or Infocast 3.5 that doesn't boot (but the screen is working), and buy it off them cheap for parts.
Duane has a small amount of Chumby devices on hand (though he did not specify whether he had any Chumby Ones) for honoring warranty replacements -- unfortunately your device would not qualify for a warranty replacement, so you would have to wait until December when the last warranties expire to seek a discounted replacement. You can read more about this in this sticky thread.
Here's a Chumby One up for bid on eBay, and here's another -- these both appear to be fully functional devices, so you might consider just replacing your Chumby One entirely (unless you successfully upgraded the flash and want to stick with that).