Everyone, stop taking guesses on how to make the playstation 3 work on his monitor, if you don't know for sure dont confuse him.
Firstly, a VGA to hdmi wire WILL NOT WORK, why? Because vga signals are analog while HDMI is digital, and that vga is NOT HDCP compliant which is a necessary feature for recieving HD signals and outputting HD resolutions.
With that out of the way: a hdmi to dvi wire WILL work since DVI is HDCP compliant and can convert hd resolutions, since there is no signal loss with DVI you will recieve FULL HD resolutions depending on your monitor. An HDMI port IS NOT NEEDED.
The problem arises with the fact that as you stated, you do not have a DVI port, only a VGA one, which is very troublesome since you won't be able to play HD. There are only two options as i see it left at your disposal:
1: Get a HD to VGA converter ( convertor is different to wire ), the problem with this is that it is expensive, around a 100$'s, like ragefury or other brands, it is full of hassle and what not and at the end you won't recieve HD videoplay ( since you are outputting through vga after all ) it is better you go for option 2
2: Buy a new monitor, you could save yourself a lot of hassle if you just buy a new monitor, one which has a DVI port, i see lots of cheap ones which cost below 10k which have DVI ports.
I hope i have helped you out.