So I was playing the new version and I wasn't having a problem with this. After about an hour I couldn't satisfy my hunger and thirst, except once. I was able to satisfy my thirst once after about 6 drink from a canteen. The hunger wasn't satisfied after eating 2 hand fulls of cereal, and 3 handfuls of sardines.
I have the problem too, I tried everything to make my character not thirsty. Scavenged a full town and drank as much water as possible and still couldn't dent the 'Thirsty' bar.
-Joined another server, and it worked. Another friend had the same problem. I'm pretty sure it is just a bug. I don't think rest really does anything at the moment, and I believe you are given an indication that you are sick which I didn't have.
This is a duplicate report and the developers are already aware of this bug/problem.
Please check the feedback tracker to see if an issue exists before creating a new one and instead vote the original one up so the developers can see it's a common problem.
You can use the 'Filter' textbox to search through existing reports using a keyword.
A list of important bug/issues that the developers are already aware of can also be found on the DayZ Forums:
http://forums.dayzgame.com/index.php?/topic/153994-early-access-important-information-known-issues/
Any additional images of the problem in question is always appreciated (if possible) and can be added by using the 'Upload File' section within a bug report.
Cheers