To whom is willing to help me,

I have 2 computers in the same room, picking up the same wireless signal, that both have the bitcoin-qt app running.  One is a new install, and the other is the original computer that has been off the bitcoin network for some time.  The new one (a MAC) is in the process of synching with the network.  The old one (a Toshiba with XP, and has coin on it) is saying that it is synching with the network, but the number of blocks isn't changing after almost an hour of running.  My question is: Is there a way of getting the coins from the old computer to the new one without trying to wrestle with making it catch up with the block count?

Thanks

p.s.  As an observation, when I attempt to close the wallet on the Toshiba, the icon remains in the task bar as before.  But now, when I right click that icon, it no longer presents the menu that would previously allow me to close the wallet altogether.  And when I go to reset, or shutdown the computer, I get the message that the program did not close properly, warning me that I may lose unsaved data.

Can anyone recommend a source of instruction on how to build a mining rig?  I have some knowledge on the components that are required, but have never actually built my own computer before.  I would particularly need to know the process of installing the necessary software to integrate the components with the operating system, along with whatever mining software may be needed.

Although I have read much of the wiki material, and probably know some of the answers subconsciously, I would appreciate some additional witnesses to the following questions:

1) I have the bitcoin client downloaded on 2 different computers.  How do I, if I can, use the same account on both of them?  For the record, I have only used one of the clients so far (to obtain, but not yet spend, coins), but prefer using the other one.  If I have to ditch one, can I transfer my coins to the other?

2) Suppose I need to do an OS recovery on my computer, and have to re-install the bitcoin client.  How do I recover the public and private keys, or are my coins lost?  For the record, I have downloaded the truecrypt program, so I can make a backup of my wallet on a thumb-drive.

3) How can I access my private key?  The only key I see in the client is the one in the receive coins page, which should be the public key, as private keys usually begin with a 5 (according to the wiki).

Thank you for your patience, understanding, and responses.