Ways to transfer old phone's contacts to a new phone without using old phone

In case the title is a bit ambiguous, I am looking for ways to transfer my contacts from my old phone to another phone, but without actually using my old phone to copy them.
Recently, my Samsung Galaxy S4's screen got bust up pretty bad, to the point where the screen is just black - thus, I got a new Ace 4 until I can afford another phone on par with the S4. The problem is that I never did any sort of backup for my contacts because I thought they were saving to my SIM card (which the first few did) but evidently they weren't and they're all on the phone's storage, as when I put the SIM into my new Ace 4 it only picked up a few contacts.
I can't find these contacts when I connect the phone to my computer, so that doesn't seem to be an option.
So to round off a few points:

• Need to transfer contacts from an old phone to a new phone - can use computer as a medium
• All contacts are saved onto the old phone's on-board storage
• Can not actually use old phone as it is broken
• Did not make and back-ups when phone was usable
• Old phone is Samsung Galaxy S4 and new phone is Samsung Galaxy Ace 4

Can anyone help?

This entry passed through the Full-Text RSS service - if this is your content and you're reading it on someone else's site, please read the FAQ at http://ift.tt/jcXqJW.

Ways to transfer old phone's contacts to a new phone without using old phone