Whatever you bought from iTunes is yours forever and can be downloaded as many times as you want. This assumes what you purchased is still available in the Store.
Here is the procedure for your reference.
On a computer, launch iTunes. Click on iTunes Store on the left
On the right you will see this
"Sign in" using the Apple ID used to purchase your songs, then click on "Purchased" (with the orange blob)
On the summary page that appears select the tab "Not on This Computer" on the right.
On the list that appears, select what you want and then click the "Download" button.
Whatever you have that did not originate from iTunes will have to be obtained from whatever means you used to obtain it in the past.
Nothing appears under "purchased"?
You are quite certain you are using the correct Apple ID?
If you are at all uncertain, start here: https://iforgot.apple.com/ and click the "Forgot your Apple ID" link. The purpose is to ensure you did not use an Apple ID that you forgot you had.
Also see if this helps: http://support.apple.com/kb/TS1408
I wish I had an explanation. The iTunes Store has a very long memory and everything you ever bought from iTunes should appear.
If you are still stuck I suggest you contact iTunes Store Support here:
Navigate the columns as follows:
All Products and Services > iTunes > iTunes Store > Purchases, Billing & Redemption
Select "my topic is not listed" to send an email to iTunes Support. Be certain to check your junk or spam folders for their reply.