Says 'Invalid DogeCoin address'

You need to do this from the wallet that SENT the transaction that is not confirming.
Internally, your wallet contains accounts, and each of your addresses is associated with one of these accounts.
In the debug window, type this to list your accounts:
> listaccounts
Then you can list the address(es) that are associated with each account:
> getaddressesbyaccount <account>
In the updated client, you can then import the address with the commands in my previous post.
I didn't follow the conversation from the start, but an easier method is just to backup wallet.dat and then update to the new client. If everything goes as expected, you should have to do anything but wait for the new client to synchronise with the network.
Currently, the transaction that you are saying is not confirming is not relayed on the network, probably because your old version cannot sync with the current chain. If you upgrade the client, it will broadcast the stuck transaction again, and this time it should be confirmed.
If you use the export/import method, and give up with the old client altogether, it will be like this transaction never existed in the first place.
What was the address that you sent the coins from? If you use the Dogecoin explorer you can look it up, and you should see that the coins are still there. They probably aren't gone, just stuck.