If I cannot exercise due to health problems, how can I lose weight?

Use up the calories! Anything that uses energy (calories) will help one lose weight, as long as he doesn't eat or drink back more calories right after the activity. Examples: if walking, take a longer route; use stairs instead of elevators; take multiple trips to and from the car when unloading groceries; park a block from school and walk there with the kids; at home, skip dessert and go walk around the block instead.
Get creative. To lose weight you need to increase your activity level and decrease your caloric intake and this can take on many forms. Some say diet is even more a factor in losing weight than exercise. Look for small ways to cut calories and only eat when your are physically hungry. Whatever you currently do, increase by just a little daily--even moving your arms & legs while seated is burning calories!