I don’t know what type of a switch your sump pump has (floating or pressure), but besides being suspended / obstructed by something inside the well itself, there might be other issues preventing it from responding properly to the water level.
Floating ball might be cracked and taking water keeping the switch in closed position
Switch located inside the floating device is frozen in one position – if you have a plastic box / container hanging on a lose wire from the side of your pump, it should make a clicking noise when moving from low to high position
Pressure switch membrane might be damaged preventing proper response
For electrical plug (pump power supply) with a small plastic tube sticking out of it (pressure switch controlled pumps) – the tube might be damaged, kinked, sealed with some debris, which prevents pressure release from the switch…
For the roots inside well
If you have an open bottom type of a sump pump well, there is not much you can do except for cleaning it periodically. In some designs this is the only way the water gets into the well (no drain tile / pipes on the sidewalls).
If there are pipes on the well sidewall, you could replace this well with a new barrel that has a bottom, but active roots will eventually penetrate sidewall openings. If they are inside the well, there’s also a chance that they contaminated drain tile – in some cases the system might require rebuilding
Hopefully this will help to solve the problem.