I'm not surprised. Though I don't know about okra, I know onions, peppers and carrots take a while to germinate. What I would do is move them away from the window to a warmer spot in your house. Until they sprout, you're looking for heat, not light, and the window might be too cool.

Also, I'm not sure about starting root vegetables indoors. Carrots are commonly seeds you direct sow, as I don't think they like to be moved. But others might have more experience where that's concerned.

Something that has worked well for me is the top of the shop lights I put the plants under once they do germinate.

The ballast puts out a nice gentle heat, and will help plants that require a little heat what they need to germinate more quickly. I've used this for two years and it works great. Peppers that used to take about 3 weeks (sometimes longer) now come up in a matter of days (5-7, normally).

I wouldn't plant root crops indoors. They are best sowed in place in the garden. To help them along, put a cold frame over them. This will help to heat the soil a bit (Be sure to vent the frame, or else you will cook the seeds) and protect them from low temperatures. This will help to reduce the time for germination, but carrots just take a while.

Okra is a HEAT LOVING PLANT. They require high soils temps to germinate, usually in the 80s.

Onions prefer to grow in cooler conditions. You will want a short-day variety, where you are, I believe.

I soak my okra seeds in HOT tap water with 1 teaspoon bleach per 8 oz water. Soak overnight then plant and mine are always UP and growing by day 3!!!