Before i start I should probably mention my PC configs:

MOTHERBOARD - MS-7525
Processor - Intel Core 2 Duo E7400
RAM - 4GB (initially it was 2GB, I  upgraded it)
Hard Disk(s) - 320GB[stock] + 1 TB Hitachi
Power Supply - UMAX SMPS 450W
GPU - Gainward GT630
Lightscribe DVD+/-R/RW

Mostly I use my PC for Watching HD Videos and browsing the Internet, Downloading and stuff.
I notice Laggs when I play Team Fortress 2, GTA SA and other games. There are sudden drops in frame rates even though V-sync is On.

My PC almost always Laggs ,sometimes it crashes showing bluescreens, and sometimes it randomly restarts itself.
My friend says its because, only '20 pin' connector is connected to my motherboard. He's saying I should also connect the 4 pin to the 24 pin socket. When i changed my PSU for the second HDD, it was some tech guy who installed it(I was clueless back then). My friend is saying the lagg happens occurs because my graphics card is not getting enough power from  the motherboard,and I should connect the 4 pin to the motherboard and replace my Power Supply Unit to a 500W one.

What do you guys think What Should I do?An adapter is available.
http://www.newegg.com/Product/Product.aspx?Item=N82E16812200064

About $7 on new egg.
If your board uses a 24pin connector, you should always have it connected.  That said I wouldn't bother trying to get an adapter for your current unit which is cheap and LIKELY low quality.  Replace it with a new power supply from a good brand like Seasonic, XFX, CORSAIR or Antec.I agree with what CAMERON stated. Also Power Supplies are not very expensive for what you need and trying to use a power supply not really designed for this hardware comes with the risk of damaging the hardware that the power supply powers. Not unless I was really desperate would I use an adapter for 20 to 24 pin connection.Thanks, I have attached the extra 4 pin to my motherboard & I will surely change the Power Supply Unit. I am thinking of buying a Cooler Master Thunder 500W, will this work?It may work, but Cooler Master is not a high end or better brand power supply. Its hit and miss as far as good ones and junk. So if going with Cooler Master its a gamble.  Thanks for the advice, I will search for a good Corsair PSU on some local stores.