2002 Nissan Maxima Car Trouble

I have a 2002 Nissan Maxima and about two weeks ago my car radio stopped working. Whenever I turned my car on the radio would make a short beeping noise and would not work. Two days after that my car wouldn't start. So I jumped started my car and took it to a auto parts store and they tested my alternator, starter, and battery. They determined that my batter was bad. I purchased a new battery and car started working again for about two days. Took that battery back and they recharged it and car stared working again for another two days and stop working again. My personal mechanic instructed me at that time to purchase a alternator and I did. He installed the new alternator and my car worked for about a day and stop working once again. Now my personal mechanic is saying that he thinks I have blown fuses or maybe an electrical problem. Could you please tell me what you think the problem may be, and the next step?