I have downloaded Electrum Bitcoin Wallet and Litecoin-QT but not sure how to upload those wallet.dat files ...
wallet.dat doesn't work just like that in Electrum.
Also wallet.dat can contain more than one address and if you you miss one address at import/export you may miss some funds at import.
First of all, for your address, you should check if blockchain.info/address/your_address shows the same amount as your wallet; if that's the case, it's easy.
(Else you have to find the other addresses you have there with funds).
Then, from Bitcoin QT console you have to export your private key(s) and import them into electrum.
I have to get my kids to sleep now, but if you are still in trouble until tomorrow - let's say in 12 hours from now - PM me and I'll try to help you with step by step instructions. I have no MAC, but at that time I will also be at the computer where I keep a Bitcoin QT and an Electrum, so I can give you exact steps (which I expect to be 99% identical for all major operating systems)
And for Litecoin it should be 99.99% similar.