How to look what you have mined in 2011 I want to get rid of an old computer, but I checked it for bitcoins, because I knew I tried to mine in the past. 
If found this

[img]https://snag.gy/YjCtkI.jpg[/img]

wallet.dat file from june 2011 

among with some other files like 

__db.001 etc.

blk001.dat 

db.log

I'm just curious if there are some coins in it. But I dont know how to access it. 
So my question is :
Do I need to download an mining program and sync with the the complete blockchain ?
Anyone an Idea where I can find instructions what to do?
And anyone knows where all these files are for?
What you need are the private keys, which are contained in the file wallet.dat.

You can access them by importing wallet.dat into a new installation of Bitcoin Core, or any other wallet client that is able to read the wallet.dat format.  You will then be able to spend the coins, if any, using that wallet client.

If you choose a wallet client which is a full node (e.g. Bitcoin Core), then you do have to download and sync the entire blockchain (currently about 130 GB).  You can also choose a "thin" (SPV) client such as Electrum which does not need to do this, at the cost of slightly increased vulnerability to certain kinds of fraud.  You can see a list of currently available wallet clients at 
https://bitcoin.org/en/choose-your-wallet.

You could also use a tool like pywallet to list the addresses whose keys are in the file, and look up those addresses on a block explorer like http://blockchain.info.  This will tell you whether you have any coins, though you would still have to import the file (or at least the keys, which you can also list with pywallet) into another wallet client in order to spend them.

All the other files store the full blockchain and transaction register as of the last time you ran the program in 2011.  You don't need these files for anything.  If you install a new wallet client, it will re-download this data if it needs it.