Normally, a cell phone service provider can easily transfer contacts and text messages from an old phone to a new phone. If the phone is broken, however, the process becomes a little more difficult. If that information can still be accessed on a broken phone, the text messages may be salvageable. If the text messages cannot be accessed normally, you may need a data cable to try to transfer text messages to a computer.
Take your broken phone to your service provider. Whether you have Verizon, AT&T, Sprint, T-Mobile or anything else, visit your nearest store.
Give your phone to a clerk at the store. Ask if the data from the phone can be recovered.
Ask the clerk if your text messages could be transferred via a data cable to your computer. If the clerk says no, you are likely out of luck.
Inquire as to the price of a data cable from the clerk. If you do not like the price, use your new phone to call the maker of the old phone to inquire as to their price for a data cable.
Open eBay if you do not accept either of the quoted prices for data cables. At the top left side of the page, choose the correct category from the list. Type in "data cable" in the search bar. A list of products will come up.
Search through the results until you find a price that you like. Purchase the data cable.
Plug one side of the data cable into your phone and the other side into your computer. You should see a folder open. Find the text messages in this folder and transfer them to your computer.
The clerk at your local service provider's store may be able to transfer all of your old data from the broken phone to a new phone on-site. If you did not save too many text messages on your old phone, you may be able to remember the information that was stored in them. If so, you can write it down. Or perhaps you can ask the person who sent it to dig into their sent archives and re-send it.
Even if you purchase a data cable and try to use it, it may not work properly. Keep in mind that the clerk can make an educated guess as to whether or not the text messages can be retrieved, but you may be wasting money trying to save them.