Your original DPaint disk may be looking for its files from the root of the volume the program was run from. If this is the case then an Assign command is futile in such cases. This is fine when running from floppy, but no good for a hard disk install (unless you don't mind all contents of the root of the DPaint floppy being in the root of of your DH0: or whatever your hard disk is called.
Instead of copying the DPaint disk contents to your hard disk root to test this theory, a workaround would be to mount a virtual floppy disk and copy the whole disk contents over to the virtual floppy, exactly as the DPaint disk. Infact, as it will be a virtual floppy you can just issue a diskcopy command. Oh, you could also mount a RAD disk instead of the virtual floppy! I should have thought of this first as it's easier!