Many BSoDs and Issues After Factory Reset

I don't have a Windows Installer Disk, but I do have the product key. I can't get to the BIOS setup because it doesn't boot when I restart my PC.

EDIT: I think that one of my RAM card is defective or a slot. I didn't do the memtest86 because I don't have a USB memory stick BUT when I turn on my computer with only 1 RAM card, the first one, it booted up.
^^ If this is not the only case, I will do the Startup repair method.

You can make a CD for memtest too.
This will tell how to make a w7 DVD or USB installer. USB flash stick are less than $10, a 4GB one is need for the w7 ISO.
Under the Note box in this tutorial.
Clean Install Windows 7

Memtest can tell us about that. Otherwise it's all guessing.

Mate might be an idea to have a look at the PSU output too.

Using HW Info

You can test the volts on thePSU with HW Info HWiNFO, HWiNFO32/64 -Download < download the rightbit version and close the right hand window select Sensors and scroll down tothe power section where you will see what the volts are doing see my pic.

The original right handwindow shows the machine running and is handy for that but for looking at the components in somedetail close it and use the main left hand side panel

FOR OTHER COMPONENTS

Open each + down into thecomponent itself and then click on it -in the right hand side will appear all sorts of details including brands speedsand other essential info that device. See pic for example.
In my pic there are only laptop volts if your system has a dedicated PSU just scroll down to the power section where it shows the rail volts.

Do you have any idea what I'm supposed to look out especially for?
I air-dusted my RAM slots, it booted and worked, but I cannot get pass the log-in screen.
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You should have scrolled down a bit more so we could see the 5V, however what's there is not good. The 3.3V should be no less than 3.1V and the 12V no less than 11.4V. The power supply (PSU) is not outputting the required voltages.

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Necessary said:

Wow, so the RAM slot isn't really defective? Just a defective PSU?
Can you recommend me the best course of action?

Rum memtest, that part is till guessing. Just run it so you'll know. It could be bad RAM, motherboard or PSU as far as we know.

I would be looking at a new PSU in any case. Corsair, Seasonic, and Antec are good quality ones. I think a 450W one will be enough.