MacBook not starting up sometimes and no startup chime when it starts

I have a macbook pro mid 2012 intel i7. The problem that I am facing is that it doesn't start up sometimes. No noise of any sort (I'm not sure but maybe sometimes the fan works). I have to keep it off for a few days and then it will again start up. Also, whenever it starts up I don't hear the startup chime. Last month I started troubleshooting it myself and found that one of the RAM module was malfunctioning. After replacing it the machine was working fine for a few days and then again the problem reappeared. I went to Apple Service center and it passed every test they had with it. They said it needs to be sent for manual testing. Could anyone here help me with this issue. Thanks in advance.

One more thing. When the macbook starts up, sometimes the system time is behind a few hours or days.

Edit 1:

No there was no liquid spilled on the system ever but I once dropped it a long time ago. It worked fine after that for about three years.

As for the RAM modules, I'll check those again and let you know. Also, is it possible the RAM holder is misbehaving or maybe PRAM is gone bad.

Thank you for your answers.

Edit 2: 18th March

The system has been working fine for past couple of days even though the start up chime is still missing. I've checked the RAM modules and they seemed fine. Still I removed one old RAM module and my system now runs on just one that I purchased few weeks ago. I've also reset the PRAM and SMC. I'll keep you posted about the performance of the Macbook. One thing though, the startup chime is still missing. Would be very grateful to know how to get that sound back.

Furthermore, there's nothing wrong with the speakers. They work just fine. Also, the service center guy booted the machine from an external HDD and still no startup sound was heard.