If you have your private key, your coins are safe.
You can redeem them for example in the CoinOMI Wallet which is available on Windows and Mobile. When you add Dogecoin, you can then swipe your private key.
I tried this and I'm still struggling, failing to recognise my private key. What does the dogecoin private key normally start with? Mine starts with '9LKEM'
Are you sure that is really a private key ? The first thing to do is to know the private key format.
There are some formats for private key, the standard one is 256-bit number in HEX and the other one is WIF format.
I think you can take some research on WIF private key format because '9LKEM' might be a WIF format for your private key.