So I have a Core i3 2375M (1.5 GHz) with 8 GB Ram. The problem is it has gone too slow I mean I have a Core 2 Duo who boot up and work faster than this thing and that is only Core 2 Duo E4600. I have tried disabling startup items and different services but that doesn't speed up laptop much. Would be appreciable if you guys help me. Thanks in advance.
Memtest is not harmful at all, it doesn't do anything to the RAM except write to it and read it back, errors in the read-back data means the RAM is faulty, that's how memory diagnostics works. The process of testing the RAM is no different to your RAM being used normally by the PC, except for the fact that the testing software is able to detect and report any errors.
Whoever told you that Memtest is dangerous doesn't know what they are talking about, and it's what any expert on this forum would recommend you use for testing RAM. I've used it myself several times. If it was potentially harmful we wouldn't be advising you to use it.