I would agree that your wood is too large and too wet. We get about 8 feet of rain annually where I am, so wood tends to be soggy and you learn where to try to find drier wood. From that photo, (which I would never have thought of it being Greece - [keep sending pics from your adventures]) I would have looked for dry wood at the base of that leaning tree to the upper left side of your photo. There also might be a bit of an undercut to the bank there. It might be just enough protection from the elements that you can find dry material for firestarting, including dry leaves. Twigs are likely tucked up in there too.
Even with a dull knife, you should have been able to fray the whittlings of your slivers even more. Stab it and rip if need be.
Depending on how wet, and for how long, yes, dead wood can get wet again, that is how it decomposes. You could take a Fir log on my soggy side of Oregon and it will decompose in a few years. Over on the dry side of Oregon which might get 7" of rain a year, it could take hundreds of years for that same log to decompose.
You can look under logs for dry spots.. even if you have to dig into the punky wood. Pull bark away from downed trees. Like ThePerfessor said, start collecting long before you want a fire. When I did SAR, we often carried road flares to have emergency firestarters. They burn at about 3,000F/1,648C and last for about 15-30 minutes depending on the flare. I am not currently carrying a road flare (although I ought to) in my BOB, but have some of these Duraflame mini logs which cost me $0.84 the other day and weigh 7oz

I also carry candle stubs. Better than just using a match or a spark.
Did you blow your flame out? I just breathe on mine when I am starting them with an open mouth, then I do not blow it out. If you are blowing on it, like you would blow on a whistle, that is too much (usually).
Did you use paper? Dry leaves? Pocket fuzz? Did you have dry-ish grasses?
To make a fire you need oxygen, heat and fuel. It looks on your particular fire, you are lacking oxygen (not stacked quite properly, too dense), heat (you were not getting enough due to lack of flame, accelerant) and the fuel was lacking, too large and too wet.
Cedar