Hi and welcome to the forum
What make/model is that new SSD drive?
And did you check your RAM with MEMTEST? as here:
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I've seen this problem on several brands of laptops including Dells. If one of your RAM sticks is faulty it could cause the problem. Your Win7 laptop is 6 years old, and the hardware is aging. You've already replaced a failed HDD and the AC adapter.
You should also replace the battery with a new one. The battery can also cause this problem. Laptop factory batteries last only 2 years, and if you've never replaced that battery since you owned the laptop; you should do so now.
If you replace both the AC adapter and the battery and any faulty RAM sticks detected, you'll be left with...