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So to be clear, there is a broiler on the top of the oven and a bake burner below the floor inside the oven. On bake and roast, the bake burner is used, not the broiler which is why the broiler will work but the other functions don't. Since your oven still works on broil, it sounds like your bake igniter is just going out and needs to be replaced. Igniters generally last about 6-8 years normally and then they either stop working all together, or they just get weak and don't draw 3.2 amps even though they are glowing. If an igniter doesn't pull 3.2 amps, the oven gas safety valve will not open up. Now the bake igniter is mounted to the bake burner below the floor inside the oven so you'd need to pull the floor out of the oven to access the igniter for replacement.
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