BSOD during everyday things, error 0x00000124

Okay to start off with, I am not a computer expert by any loose translation of the words. So please break things down for me. I have had several BSOD's. With different error code extensions but they all start with the primary error code of 0x00000124. I do not know much about the computer as it is a custom-built-hand-me-down. I got the computer in August of last year, supposedly completely updated and rebuilt. In December I started getting the BSOD's. At that time I had not installed anything new, that I am aware of, other than the standard Windows updates.

I have checked the core temps and all seem to be running around 35C-42C, depending on how long it has been on. I dusted the entire computer out after the initial BSOD and several times since then, as I have been told that it is overheating due to being dusty. Upon initial dusting, I found the CPU fan unit was loose. I put new thermal paste compound on it and reseated the fan unit. I have checked and rechecked that everything is seated correctly, firmly, and snuggly. I replaced the power supply -- I know for a fact the old one was over 10 years old -- with a Rosewill.

Any information that I know about the system I will list. I do know that shortly after the BSOD's started I downloaded a new antivirus system. I do not know how to look up the name of it and I can't remember. From the angle at which my hard drive is seated I cannot read the make or model number of it.

The initial BSOD just had the error code:
0x00000124

Two of the other BSOD error codes are as follows:
0x00000124 (0x0000000000000000, 0xFFFFFA8004C60028, 0x00000000B20000040, 0x0000000000000800)
0x00000124 (0x0000000000000000, 0xFFFFFA8004A3E028, 0x00000000B20000040, 0x0000000000000800)

It will not always BSOD though. At times, it will freeze up for about 20 seconds and then unfreeze but my graphics will be weird (i.e., my mouse icon will be very large, yellow, and shadowed; or it will be regular size but a very light yellow that is hard to see). Once this initial freeze/unfreeze happens, all processes slow down drastically until I am forced to reboot the whole system just to get anything done.

I need this computer desperately right now and could use any help you can offer. I fear that it is a fatal CPU issue, and cannot afford to replace it right now. Any programs that I download to fix it need to be free if at all available as I do not currently have a job. If there is any information that you need, I will do what I can to find out said information for you if you can tell me how to retrieve it. Please help ASAP as I am in an online college and need my computer to operate smoothly to attend my classes. Thank you in advance.

If there is any information that has not been included in this post I will include it asap.