Not knowing what your house is like, have you checked behind everything in the basement (or cellar), each closet, under each bed and behind shoes, boxes, under the sink (kitchen cupboards), chests or trunks that might have been open when she disappeared (she might be locked inside), behind the piano (if you have one), behind the entertainment center, fridge, stove (warm back there), etc.?
In, under, around, and inside of everything conceivable in which a cat might hide or be trapped. There have been stories of cats living inside the couch for weeks without being discovered.
Also, cats are notoriously quick and can escape the house between your one-two strides it take to get out the door, and you don't even see them...! Ours play this trick on us at time. She may have gotten out. "All the doors and windows were closed when she disappeared" only means that everything was closed at the time you determined she was missing...
How old is she? If she's old enough to go into heat, she might be out seeking a mate. 4 weeks isn't much time to remember where your house is if she's only been indoors all that time, but if she's mating, she might return.
Be sure to check around the neighborhood calling her name often, if she's accustomed to hearing her name and your voice. With your neighbor's permission, check under and around everything, she could be living under a porch or in a dust bin, or hiding in a neighbor's garage.
Meanwhile, if you believe she is in the house and is free to move about as she likes, leave food, water, and a litter box inside where she can use it, as well as in the garage.
If she returns, please let readers know, and how she turned up (where she was, etc.).