I have been experiencing this problem in my 1995 Civic DX for a few years.Sometimes, while driving, the car would start making beeping noise, as if the door was open. Also, the windshield wipers would stop working when set on the interval. I played around with it and what I found is if the noise starts, or the wipers interval is not working, I would just press on the fust box, and it goes back to normal. But lately this is happening a lot more often, and pressing on the fusebox doesnt really fix it, maybe for a few minutes tops. I wonder what it could be, whether its something inside the fusebox, or a connection to the fusebox.

 

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It sounds to me that if pushing on the fuse box solves the problem, then you have something that is loose in there. I would just take a look inside that box and see if you can find something obvious. Other than that, I am all out of ideas.