What are you using for a cable? The DP-01 has unbalanced 1/4" (6.3mm) inputs. (DP-01FX does have XLR's) The SM58 has an XLR connection. Wrong cable (not wired to transition from balanced XLR to unbalanced 1/4") may prevent signal from getting into the DP-01.
Does the DP-01 see signal from an electric guitar or other source?
Assuming your SM58 worked before and then suddenly stopped........unless you dropped it pretty hard.....(VERY HARD)......it's likely the cable. If the SM58 is new and it never worked.......that's different.