System needed to be troubleshoot

First kindly note my current machine specifications:
Lenovo ThinkCentre M58p Type 7484 Tower
Processor: Intel Core 2 Duo E4600 2.40GHz/2M/800
RAM: 2*2 GB (4GB) DDR3
Hard Drive: 320 GB Samsung
Chipset: Intel Q45/Q43 Express Chipset
Windows: Windows 7 Professional 32-bit SP1

Yesterday I started my system as usual. But It won't display any thing & beeps (Short/Normal) 4x4 times with both fans (CPU & System) run at full speed then I forcefully shut it down with power button (Long press), Furthermore today I tried many times it does same thing (As mentioned above) one time & then second time it works as usual, but even second time fans (CPU & System) still runs at full speed. I have also searched on the internet before posting this thread, it probably indicates an issue with RAM, but I test both of my RAM(s) with my neighbor's computer, it works very well & also checked my system with my neighbor's RAM(s), I didn't understand that if I plug in the computer it runs well but fans work at full speed one time, but another time it starts beeping as said before. My processor's heatsink was already cleaned due to low dust area & HDD health/sector check gave me a clear report. Due to this type of malfunctionality I reflash the same version of BIOS (latest) (As available on official site), but none works.

Kindly help me out ASAP, as I'm a student & needed to complete my assignments shortly.

xrobwx71 said:

Just so I'm understanding, can you turn it on and run apps?

How did you test the RAM? Simply plugging them in and observe them working or did you run a test program like Memtest?

Please continue with Malnutrition's suggestion.

Click to expand...

Yup! I tested just after when the problem occurs, as I said before in my original post that I do a research on internet & It also refers me to check out RAM(s), So it couldn't be problematic issue with RAM(s) (I also test both of my RAM(s) with my neighbor's computer, it works very well & also checked my system with my neighbor's RAM(s)).

Actually I didn't understand that why the system runs well one time with one problem (fans run at full speed), but on second time it start beeping. At the last if I slept out system when it runs well then upon log on it didn't starts but acts as second time means beeps 4x4 time. I couldn't figure out what is going on with it.