I finally found the backup I wrote down after using Gavin Andresen's Bitcoin faucet. I don't remember if I was using only Bitcoin Core, Armory, or something like Multi-bit. Those sound familiar.
If the backup private key was generated from the year 2009 to 2010 I'm sure it was not created from Armory or multibit wallet because these two wallets was announced between year 2011 and 2012.
Thanks for the information. The public address starts with a 1 and here it is: 1DYFqhdKDkHYytVn66QWKGY4PUebNYH9j9
The character starts with most likely an A or 1, but read another way these are the first three 001.
If it starts with 001 then it's a binary format you might need to covert it to the WIF key format to be able to import it to other wallets like Electrum