Dell Inspiron 1545 Freezing.

Check if your fan is running at least 2800rpm and if the temperatures don't exceed 70 celsius. If your computer is heating up that might be the cause for either freezing computer or it getting shut off at random. If this is the case then clean it up with some compressed air and check if that helps.

I see, so the temperature seems to be okay. Well then lets check if this is software related by opening up the task manager (ctrl+alt+del) and checking for any programs that are not responding. If you find any make sure you have the latest versions of them. If this was not the problem then your video driver might be the problem check on device manager if there is any red marks showing up next to the drivers. Since you have received a message concerning the drivers before this might be the problem. If all above has failed to recognize the problem then your problem will be hardware related (although seems doubtful from what you have said previously) but it could be the ram, or cpu. Since your computer is not yet turning off i cannot conclude that the problem is motherboard or power supply related. Let me know if any of this worked.

I request you to check once again if the HDD is detected in the BIOS. For that, restart the system and at the Dell logo keeping taping the F2 key every two seconds. In the BIOS screen click on the ‘+’sign to the left of ‘General’ and then on ‘’System Information’, check what is listed for Primary Hard Drive.
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I suggest that you to run custom test on the HDD. To run custom test restart the system and at the Dell logo tap the F12 key every two seconds. This will start the One-time boot menu. Using arrow keys select ‘Diagnostics’ and hit enter. This will run diagnostics on the hardware components of the system which may take around 5 minutes. Next Press N for no when it asks you to continue Memory test.

Next the option listed will be: ‘Test Memory’, ‘Test System’ and Exit. Please select ‘Test System’. Then there will be option to run ‘Express test’, ‘Extended Test’, ‘Custom Test’ and ‘Symptom Tree’. Select Custom test and click on Hard Drive and hit enter. This will take a while depending the size of the HDD. Reply with the status of the test for further assistance.