How dead is dead? Dead as in it has to be plugged in to charger to power up? Or dead as in needs to be in a zip-lock bag?
In the interests of avoiding a repeat of contact loss, regularly export your contacts to the SIM or SD card. I do this with my Android phone on a regular basis, having nearly lost everything when my previous phone got caught between a jeep and a hard place. Contacts-the 3 square menu thingie- Export Contacts . Then on your new Android device, insert SIM card, follow the same process and Import Contacts.
The phone manufacturer may have rescue and recovery software that you can use from a computer to backup, recover or migrate your entire phone to a new device of the same manufacture. I use Xperia Companion from SONY for my phone. Not sure what other manufacturers offer the same kind of support. But the phone has to power up - if you can't coerce it into turning on, it gets more difficult.
There is always the repair shops, you never know what some of these tech guys can do. Maybe not the screen replacement guy at the Mall kiosk, but maybe yes.
No electronic data is truly lost until it it shot with a silver bullet, shredded with a mandoline forged from a nickel-iron meteorite, and the remaining pieces burnt using a fire of Siberian Larch under the light of the third full moon since a full solar eclipse. I got these instructions from a Russian, they know.
Is your phone android or iOS? Most methods would require a computer and some sort of program. This site offers options for android as well as iOS. Disclaimer: I have not personally used that site or program so I do not know how well it works. If you do a search on Google, there may be other suitable options available.
Hope this helps 😀