S-Video is garbage, don't use it.
You could get a HDFury, which is an expensive HDMI to component video adapter, which will maintain HD resolution in the conversion.
You can also try the DVI connection on the projector. While the DVI connection is not HDCP compliant, the PS4 may allow for games to be played across it and not have HDCP restrictions. I'm not sure though and certainly movies will have HDCP encryption.
The projector you have is the first one I owned as well and is now well over a decade old and very outdated. It's unfortunate that it is the case, but it is time for a new projector to be considered instead of a Band-Aid. You can find some used 720p projectors (shop carefully) online for not a lot of cash. Heck, brand new ones are about $500 which isn't a bad price. Still, I realize this isn't something that may be in the budget right now.
While this sounds like something you want, you want to be very wary of this type of product:http://www.atlona.com/Atlona-HDMI-to-VGA-Component-Stereo-Audio-Format-Converter.html
It says specifically: "NOT HDCP Compatible"
And that's a huge issue!
The HDFury is HDCP compliant so it is supposed to work, it's not inexpensive though.http://www.hdfury.com/buy-hdfury-now/
$250 on the 'cheap' side.
Seems like this would make more sense:http://www.ebay.com/itm/Panasonic-PT-AE900U-LCD-Projector-/181259854416?pt=US_Video_Projectors&hash=item2a33ede250
Still, used, so you are taking a chance.
But, this is the modern era of 720p projectors...http://www.projectorcentral.com/Acer-H5370BD.htm
Under $500 for a HD projector with Full 3D support, and a long lamp life to keep budgets in check.
- Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.