If you are unable to download past purchases again there may be restrictions on some of that content, I would suggest getting in contact with the iTunes Store Support Team via...
iTunes>iTunes Store>Purchases and Billing>(Select the most apropriate topic or type your own)>Prefered Contact Method
...and ask them the same question. They have access to see all of your billing history etc and are in the best position to answer your questions.
From iTunes Menu Bar...
1) iTunesè Preferencesè Store è Check "Music" under "Automatic Downloads" & check "Show iTunes in the Cloud Purchases"
2) Store è make sure you are signed in and the computer is authorized. From here, you may select "View account" and then have access to purchases history. You may also select "Check for available downloads" now.
Not all past purchases will be available for re-download for all time.
For example if the copyright holder of an Album (which is not Apple, they are just the retailer) decides to reissue an Album they might remove the items you originally purchased from the iTunes Store. This will also remove those items from your purchase history. The copyright holder may then give Apple another "version" of the Album that may appear the same as the items you originally purchased, but because to the DB they are not the same items you will no longer have access to those items in your purchase history. This is just one example.
This is why it is your responsiblity to download and backup all of your purchases locally. Ideally to an external HDD, or perhaps a dedicated cloud backup solution. The iTunes in the Cloud service provided by Apple is not a backup service, nor do they advertise it as such, so it should not be depended on to be.
As to getting your personal data onto your new Mac this Apple KB article can help: http://support.apple.com/kb/HT1408?viewlocale=en_US&locale=en_US.
Now that you have a Mac I strongly recommend you purchase an external HDD that is at least 2x the size of the internal HDD (preferably 3x) and start using Time Machine to backup all of your personal data.