Radish and lettuce should have sprouted already (you have some), carrots need darkness, I believe, to start growing & take longer. Not sure about parsley anymore I buy a start or 2 rather than start from seeds. I grow many veggies from seeds otherwise. Did you check how warm soil should be for them? (I never used set you mention, just planters and outside beds).

The planter area is not deep enough for carrots.

I will try radishes and lettuce. Nothing else has worked, so far.

This year I am using my own mixture of potting soil since my failures last year might have been because I was using an inferior brand of potting soil. I planted lettuce, radishes and carrots and filled the pots up to the brim to allow for settlement. Everything has germinated.