Does your LCD monitor have an HDMI input? If you are using the standard analog connections (S-video, composite, component), the monitor does not have the inputs for those, only VGA and DVI. However, if it has a DVI input you may be able to get an adaptor that takes the PS3's HDMI to a DVI adaptor to its input on the monitor (http://www.amazon.com/BlueRigger-Speed-Adapter-Cable-Meters/dp/B004S4R5CK/ref=sr_1_4?s=electronics&ie=UTF8&qid=1415348692&sr=1-4&keywords=dvi+to+hdmi+adapter). Sadly though, the PS3's HDMI output is encrypted via HDCP and your monitor through its DVI input does not comply with such protection.
Option B would to get a converter that sends your analog video signal (composite, s-video, component) to a VGA or DVI connection to your monitor (Composite/vga box: http://www.amazon.com/Video-Composite-Monitor-Converter-Adapter/dp/B00K3OT2P2/ref=sr_1_1?s=electronics&ie=UTF8&qid=1418269256&sr=1-1&keywords=rca+to+vga+converter) (Component to vga converter: http://www.amazon.com/Monoprice-107113-Component-YpbPr-Converter/dp/B009GUQYBO/ref=sr_1_1?s=electronics&ie=UTF8&qid=1418290917&sr=1-1&keywords=component+to+vga+converter).
Keep in mind for option B that only the video signals are sent through VGA/DVI, as they do not carry audio to you monitor. You would need to hook up the systems analog audio to a speaker system, or if your monitor has audio inputs (headphone jack) you would need to get another adaptor that takes the red and white L//R into a headphone jack input.
As for graphics, if you send s-video to the VGA/DVI converter, it would look worse that it was on your old TV (whatever it was). If you send component through the box in mind though that if you use component on the PS3 @ 1080p and the box is not the upconverting type that adjusts the signal to your monitors max resolution, you need to set the PS3's output to 720p to get it to display. Under the component feed, video quality would be pretty good but not to the level of HDMI on a HDTV.
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