can I tranfer files from an imac with a black screen to a new imac?

When the new machine arrives BEFORE TURNING IT ON for the first time, connect the Time Machine backup from the old computer via a USB cable. When you turn on the new machine, it will eventually get to a point where it is asking if you are migrating from an old Mac to a new one, select YES and follow the on-screen directions.

Any old 32 bit apps will not migrate, Catalina will only run 64bit apps. If you use any Adobe or Microsoft apps they will need to be manually installed as those developers do not like their apps to be migrated.

Your photos (even if they are in a iPhoto library) are okay. Simply connect the drives that have the photos on them and you can import the libraries into the Photo's for Mac app.

Possibly, however the smart thing to do is to connect the old Mac's Time Machine (or bootable clone External Hard Disk) to the new iMac via a USB cable. Then launch Migration Assistant (Applications - Utilities - Migration Assistant) and migrate your data. This is the most reliable, quickest and easiest method.

If you don't have a backup of the old machine (VERY VERY foolish) then you can use Target Disk Mode to copy data. If the old Mac is dead then the next thing to try is to remove the HD from the old Mac put it in an enclosure and then use Migration Assistant that way.

Your welcome.