Blank display

Let's see if I have this right. Normally, your monitor is plugged into your 8600GT, but sometimes it does not come on when you turn on your PC; if you move the monitor connector to the onboard VGA adapter, it comes on then? But not if you move it there when the 8600GT is working?
That suggests to me that in those cases, your PC is not seeing the 8600GT. Open your case, and with the PSU switch turned off, remove and reseat that 8600GT. This would also be a good time to clean the dust out of your PC; use a can of compressed air, not a vacuum cleaner (which can generate static). Turn your PSU back on, and see if that makes a difference. If so, great. If not, the video card and/or mobo may be failing, which would not be too unusual considering their age. The good news is you can replace both with comparable but better for around $100. The bad news is you would probably need to reload Windows (and therefor all your programs). Also, that $100 USD price may be wishful thinking as I believe you are in India, where prices may be a lot higher and availability a lot lower.
Do you play any games? If your 8600GT has been working well for you, a HD4650 would replace it nicely.

Thanks this advice did solve my problem and you got my question straight right ur talented man! . ya i am gamer games like cod, farcry i prefer to play. well game comes cheap in india (i am not talking about pirated ones ) for ex:\gta4 can be yours in just 10$ according to indian currency .

Glad to hear it. It is nice not to have to spend any money, although your 8600GT would be outperformed significantly by a HD4670 or even a GDDR3 version of the HD4650 (the GDDR2 version will only be slightly better). Neither of those needs extra power either. If you want something stronger, we'll need to know more about your PSU to see what it can handle.

i have joined ants( animation course). so i wanna upgrade my gpu . i am currently using this mobo:\ http://in.asus.com/product.aspx?P_ID=PYvbfOokwxUzJky3&t...
i am bit confused which gpu i should go for nvidia or ati . and pls suggest which gpu will be best with this mobo . my pci-e has 1.0 slot.

my motherboard:\ p5gc-mx/1333 asus

Well, it depends what kind of animation you are doing. You may find the 8600GT is quite sufficient. Ask whomever is teaching the course.
PCIE 2.0 is backwards compatible with the PCIE 1.0 slot you have, so there are no currently available cards that you could not use.

hmm...
This 8600gt is outdated more over it dosent have inbuilt cooling gpu fan attached to it and this increases my system temp. sir, which card would u suggest me.

Speak to the person teaching the course for specific recommendations, but if you're not also playing games, something like a HD4670 would probably be decent; not too expensive and doesn't need much power. Anything more, and I'll need to know more about your PSU, including brand, model, and # of amps on its +12V rail(s).