If your sump pump does not activate it is most likely gunked up (technical term, sorry). You can try some methods suggested on these forums to unstick it if you find anti-freeze backing up thru the drain like pouring in hot water or vinegar to free things up. Of course once your drain is overflowing its going to be messy trying to get the sump empty again so you can add those ingredients. I suggest you open the sink cabinet and remove the floor piece - mine just lifts out, no fasteners. The sump (i.e. bilge) pump should power on when the box is about 3/4 full. If it doesn't it may be time to bite the bullet as I did before things get messy.
I took the lid off which as others have acknowledged is a pain but with patience and an offset phillips head driver its pretty easy since the material is all plastic. Then try flicking the manual lever of the bilge pump UP (its located on the far side of the pump and out of sight so just play around a bit) to activate the pump. If that doesn't work just get a small cup and remove the water manually. I then disassembled the cylindrical filter and cleaned it, removed the pump (left all wires in place and only had to remove a zip tie that gathered extra wire) and cleaned it with a toothbrush, cleaned out the box, clean the one way valve in the hose exiting the box, and finally tried the manual lever again. All the fittings in and around the box are tight so write down your order of disassembly to make reassembly easier. If after all the cleaning the manual lever doesn't activate the pump you probably have a bad pump or more likely an electrical issue to chase down.
If the pump does finally activate reassemble everything, pour in about 1/2 gallon of vinegar (do not put in enough to activate the pump) and let it sit for an hour or two. Then flush with water.
Here are some pics to show what I did:
Sump box with view of pump, filter, inlet and outlet:
https://share.icloud.com/photos/08yiTQg ... QCchQj9Aew
Sump box lid removed:
https://share.icloud.com/photos/0iNV8Su ... yMNti6E6zA
Pump close up:
https://share.icloud.com/photos/04zuMdg ... C2OZE2yrYQ
Float switch close up (the manual lever is behind the switch in the upper right corner):
https://share.icloud.com/photos/0Hhl6h_ ... ANKxWhYBfQ
Filter removed:
https://share.icloud.com/photos/0mxi792 ... -pihp_b__g
Pump removed (the one way valve is the dark bit in the short plastic tube):
https://share.icloud.com/photos/0_-3LyB ... PHjz1LW1yw
Hose clamp for the short plastic tube (pain to remove it but easy to put on):
https://share.icloud.com/photos/06RRpV6 ... lORnk8MxdQ
Float switch removal (only need to remove the visible screw, the out of view screw just needs to be loosed 1 turn):
https://share.icloud.com/photos/0HymzCP ... PMqyP2m_dQ
The out of view screw can stay in place:
https://share.icloud.com/photos/0LHNLty ... ePueshnMrA
Float switch removed with float mechanism slid out of the case:
https://share.icloud.com/photos/0eg3zBD ... -NJk9h5SZQ
HTH, GF