True Image 2013 lost on broken machine.

Until recently, I had a 32 bit Vista machine with TI 2013.
The pc broke completely - including power supply and motherboard.
As a temporary measure, I now have a 64 bit Windows 7 machine which came with not much on it including any of mine i.e. pictures, music, documents, emails.
Prior to this disaster, I took:-
1) Weekly incrementals of the whole C disk with a new full one every 5th week. These went to an external hard drive which does still work.
2) Daily online backups of most/all of my User files/folders as per the i.e. above on a monthly 50gb subscription.
Now then:-
a) Can I download my old 2013 product again to this new machine?
b) If not, do I assume I have to get/buy 2015?
c) Either way, does anyone know of a problem getting my User stuff back whichever version of TI I end up with?
ps
The current machine has the same 500 gb sized disk, more storage and a faster processor if any of this makes a difference.
pps
If anyone cares to look at this, simply expressed answers would be appreciated as my pc expertise is only marginally above appalling.