Mainly due to utter curiosity I purchased 0.5 bitcoin in 2013 and I have a piece of paper with 3 different passwords on. however, I've recently opened the wallet I had the coin in, but nothing shows up! Neither does it ask me for a password? I've searched around for knowledgeable individuals who can guide me - in very layman terms - as to what process I need to go through in attempting to retrieve this 1/2 coin. As I'm very much in need of getting rid of the 1/2 coin I shall be more than happy to financially reward any person who can successfully retrieve it.
First off: DO NOT send those exact passwords to anyone offering help. Having those passwords may allow them to access and steal your coins.
If you open your wallet and see a zero balance, that is probably not a good sign if you haven't moved the coins yourself. Look at the history of transactions, and see if there are any that moved the coins to a new address. You need to figure out if the bitcoin has been moved to an address that you no longer control.
Chris, Did you go to blockchain.info and copy/paste the public address of your wallet into the search box in the top right-hand corner of the screen? This will let you see the amount of bitcoin assigned to that address on the blockchain itself, so you don't have to wait to download the entire thing. If you have done that and it shows zero bitcoin we probably have two scenarios; theft or its the wrong public address for the wallet. If it does show your 1/2 BTC in there you will need the private address to import it. I'd recommend opening the account in blockchain.info, since it just references the blockchain instead of making you download it. If you have a blockchain.info accoutn you can import your 1/2 BTC wallet using the private address at this location... Settings -> Addresses -> + Import Bitcoin Addresses -> Import Address -> put the private key in the box -> Import -> Close
The information provided is quite vague so I will provide my assumption as to how to resolve it. It sounds as if you have a paper wallet. Paper wallets have a public/private key pair. In your post you mentioned a third piece of information which might be the seed of the wallet.
First step, search the public key on a blockchain explorer (blockchain.info or tradeblock.com are good choices). There you will see all transactions associated to the wallet.
If the balance is 0.5 then it is just a matter of importing the key pair into a wallet (this can be done through the mycelium wallet). You can also YouTube how to sweep a paper wallet for more information about importing the key pair.
If this answer doesn't help then you need to add more information about the paper that you have: how long are the "passwords", are they a combination off all characters, are they words or public/private keys.