Be patient, most will come up in it's own time.
I tend to start my veg off in pots, to stop it getting decimated by slugs. Carrots and beets go straight into the ground, but peas, beans, cabbage, sprouts etc all get started off in pots - they're generally warmer than the ground at this time of year, and you can place them on gravel, or high up, to make sure that slugs can't get at them.
Don't get too disheartened. It may be that the ground is still a little cold for them to peep through, the fact that you have peas, beans and carrots coming through is promising! If all else fails, you could try getting some plug plants from the garden centre, or re-sow some of the things that haven't germinated in pots this time.
You may also need to protect the green shoots from birds at this time of year, it may be worth investing in a mesh mini-tunnel, to protect them whilst young & tender, once bigger than about 6 inches, they lose their appeal to birds.
Get yourself a big planter/window-box, put rings of copper tape around the top to deter slugs, and plant yourself some lettuce, radish, carrots, anything else you like to eat salad-wise, pop some seeds in and put it by the back door (if there's room and it's sunny enough). Quick crops will keep you going until some of the staples come through.
One thought, did you 'chit' the potatoes when you put them in, and have they gone into the ground, or did you put them in potato planters/tyres? Did you enrich the ground before planting anything? Carrots will grow in almost anything, but beans are very greedy.
Get yourself a copy of growing veg month by month by John Harrison. It's only a fiver or so from amazon, and it's become my veg bible. Has lots of great ideas, and will keep you going when disheartened. You will learn what will grow and what won't, it can be a steep learning curve when starting out.