Laptop restarting itself

Hello i have an inspiron 1440. In April the charger port broke and i had my laptop sent in to be repaired , which they did. The only problem is that now my computer restarts randomly and i no longer have a warranty. There is no consistency for when it restarts. Sometimes my charger is plugged in sometimes it isn't. Sometimes it is at the very beginning sometimes it happens after four or five hours. It is not overheating. The charger i have is not the original charger either because my original one broke. I did the diagnostics that you can run from the startup screen four times. The first time it said the memory integrity test failed the second test said nothing was wrong the third test said nothing was wrong and the fourth test the memory integrity test failed. I did the tests on separate days. I don't have any trouble booting windows 7. When the computer restarts, my screen turns black and a hear a popping noise that usually here when the computer turns off. When i turn my computer back on and/or when it restarts itself a screen turns up and says that i turned off my computer improperly and if i would like to run it in safe mode.  I have run virus scans and the malwarebytes picks up pup.mightymagoo and i deleted that but it keeps coming up. None of my other virus scanners picks that virus up and that is about all i can say about my problem right now.