Well it will depend. Were the contacts on the phone itself, or on the SD card? If the latter you just need to connect the card to a different device. If they were on the phone itself, then it is going to depend on if you can power the phone or not, and how damaged it is.
If you can get it to turn on, you may be able to get the contacts by connecting it to a computer via USB and locating the correct file and move it over to the computer. It can be a .db file or a .vcf file.
If neither of those will work, you won't be able to get them off the device.