There's about 78,000 pictures of LAPD cars and equipment on flickr.com from various dates. You can filter image "taken on" dates by clicking "Advanced" and "Date taken". So, for example, you can make it display pictures only taken between 2001 and 2007.
I've done a lot of searching before, and I don't believe I've seen an LAPD Caprice in service past 2003 or 2004. They didn't keep them in service that long.
The latest picture I could find of an LAPD Caprice was photographed on March 1st, 2008:
https://www.flickr.com/photos/southerncalifornian/2311889844
I'm not sure if it was already decommissioned in that picture, but the poster referred to it as a likely "boneyard" for retired vehicles.
For an example of a Caprice that was definitely confirmed to be in service in the later 00's (for a large city) the NYPD had one in service in 2006:
https://www.flickr.com/photos/14968334@N00/142469658
Other vehicles from the older years you're looking for can be found on flickr, but I most commonly see the Crown Victoria being used in 2004, to answer your question. The LAPD never really experimented with tons of makes and models, as the NYPD did.