Are you still using the same Apple ID and password as was used to purchase the Apps?
Apple purchases are forever linked to the Apple ID used to purchases them. You can change you Apple ID if you email changes, but making a new Apple ID will cause you to lose control of the previous purchases.
That's not exactly true. You would still have control over those purchases. They would remain tied to the original ID and you could still log in to that ID and download those items to your current devices. (I have my original Apple ID from way back when the iPod mini came out...the original, no color screen version. I haven't had access to that email in maybe 10 years yet I still have access to that Apple ID and can still download those purchases).
That is if, and only if you know your old Apple ID. Apple forums are full of people who forget original Apple ID, make a new one and then are upset about losing their old music and apps.
I suppose it's possible to forget what email you used (although it shouldn't be too hard to go through a process of elimination). Even if you don't have access to that email address anymore you can still contact Apple to gain access to that account. Again, this is what I did. I think it's more likely that you no longer have access to the original Apple ID email address than it is to absolutely not know what the email address was. If you still have access to the computer that has the purchased items on it from itunes (even if the computer is no longer authorized to play the items) you can look at the info for the file and it will show you the Apple ID it is associated with.