When do I give up?

I have a Arduino Nano that I have been using for experimenting with (temperature tester, ssd1306, etc). I was using it to test different fonts with a SSD1306 when after a few times, it just quit. I tried to run the blink program, but
got the dreaded:
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x4d error.
Of course, I looked the error up on the internet and found that the processor might be the error so I changed it to ATmega328P (Old bootloader) and no luck. I changed it back and no luck. I tried
several things including making sure that the Arduino AVR board was loaded with the latest versiom (1.8.2) was installed but had no success.
So I am at a crossroads. I want to understand why the nano is not working but having devoted over 3 hours at various times to try to fix it, I was thinking of
a) pulling the parts of the board and scraping it
b)try burning a new bootloader on it (if that is an options
c)you tell me.

Even though I have several in my parts bin, it is driving me nuts that I can't figure it out.

It depends on several factors which only you can determine:

  • How much is your time worth? For example, if you value your time at $10/hr, then you have already expended $30 worth of time trying to recover a board that can be purchased for less than that.
  • How much do you value the knowledge you gain from attempting to recover the board? Even if you spend ten hours and still can get the board working, you may gain extremely valuable knowledge along the way.
  • What is the entertainment value of the recovery process? I will sometimes try to fix things even when it's not economically sensible simply because it's a fun challenge.

From the symptoms you describe, it's most likely the board is destroyed. The parts probably aren't even worth the effort to salvage.

I would certainly try burning the bootloader, if only for the sake of curiosity, but it takes me less than a minute to burn a bootloader because I have an ISP programmer within arm's reach and know the procedure by heart. For someone who needs to wire up an "Arduino as ISP" programmer, figure out which sketch to upload, which programmer selection, troubleshoot the wiring when it fails, etc..., it may not be such an easy process. But again, you might learn a lot from doing it and have some fun.

@Per +1

I went with option 2 and re-burned the bootloader on the bad nano. I looked on the internet and found several sites that showed how to do it. I chose:
After a couple of attempts, it worked and now I have a functional nano board again. I probably have 3 or 4 hours trying to make it work. Was it worth it? In dollars, no. In education, yeah, I would say so. In saving the environment by not disposing in a landfill, temporarily (when I'm gone, my kids will eventually pitch it in the trash. But I do have the satisfaction of making it work again. Thanks to all who answered my post.