If the shutdowns aren't a direct result of heat, it could be a RAM module or hard drive failure (both of these are cheap & easy fixes, though), especially if the components are regularly running hot.

So long as you have the wallet file on the hard drive (and I wouldn't trust that hard drive until the problem's figured out) and it's created the priv-pub key to give you an address to receive at, there's no risk in sending coins to those addresses.

The weird behaviors can happen if you clone a wallet and use it on 2 different computers.

This is mainly because QT wallets have a default pool of 100 pre-generated addresses (the 100 next addresses it will use as change or show you when you click on "new address" are pre-generated). Each time you use up an address from that pool, QT creates a new (random) one to keep a 100 pool.

So if you clone a wallet to another computer and use both, you'll have the impression that they are syncrhonized, until you reach the point where you used up all 100 addresses from the "common" pool, and they begin to use random address from the "fresh" 100 pool each one will have created on his side.

What you are doing here is different. You just backed up a wallet, and created a fresh new one, not expecting that they behave the same way.
So don't be afraid about that warning.

Also, you cannot specify the wallet.dat filename when running QT, so you'll have to rename/copy/move your new wallet before copying back the locked old one (and renaming it wallet.dat if necessary), before next password cracking session.

To learn more, you may simply search in this sub for material about QT wallet.

That is the simplest way, use blockchain.info

You will see your balance update + the incoming transaction when you synchronize your bitcoin-qt wallet.
But the coins are already at your bitcoin address (you checked at blockchain.info, blockchain.info is always synced), just your bitcoin-qt does not know it yet.

As long as wallet is encrypted securely, you can push it to any cloud service, too (just rename the file not to hint about what it is), or just print the private keys and hide them under your bed.
My point was : don't rely exclusively on a usb stick as a safe backup.

You had the bitcoin-qt synced back in April. Today transaction you made has 21 confirmations at blockchain.info, it means in your bitcoin-qt must be downloaded all blocks (might remain 21 undownloaded blocks) so you can see this transaction + balance update

it must be blockchain downloading, be patient.

Sorry didnt read your 1st post carefully
Synchronize your wallets on your computer, both Litecoin-qt and Bitcoin-qt

You cant send Bitcoins to Litecoins address and vice versa.
Bitcoin address start with 1xxxxxx
Litecoin address start with Lxxxxxx

I think you can download pywallet to see your privates key in the one unlocked

You can post here your address and/or the transaction id so we can check. It's safe noone can have access to your coins with those informations.

Maybe you can show the transaction ID?
Did it get confirmed?

It depends on how much transactions and addresses it contains, but most likely you'll be able to store 1000 wallets at least on such a key  
Keep in mind usb sticks tend to have a very short life span, though, consider other backup methods too.

What do you mean?

You sure you have private keys and not addresses?

Address (note the begins with one and is generally shorter than a private key):
14CD3Ra5yMjWaEA3HTX5nAqvYb8sSjMheJ

Private Key (one format could be in an alternate form):
5KEWNTr5Jsk4H147KkNE2NZTg9zXESU5m6rmibfJQMvMswL6WiZ

If you have private key.
1) Don't share it with anyone.  Access to private key = ownership for all practical intents and purposes.  If you give someone the private key so they can help and they steal your coins they are probably gone.
2) As indicated above you can import the private key into any wallet, even a new QT client wallet, an eWallet, or a different client and gain access to the funds.

If you have the address not the private key then you have nothing. Addresses are public knowledge.  The private key is what allows the owner (and nobody else) to spend/move coins.

It's most likely your bitcoin client. To reassure yourself, check out the listing on blockchain.info for the address that is supposed to receive bitcoins.