Welcome to the forum!
Dolby Pro Logic only requires a two-channel connection, so you can still get that if your new DVD player has left/right analog audio outputs. Just connect the those two outputs (assuming it has them - I'd be shocked if it doesn't) to the receiver, and you're set.
If you want Dolby Digital or DTS, you'll need to utilize the digital connection. To go from a digital audio connection (like the digital coax on your new player) to six-channel analog, you'll need a processor for the codec (DD or DTS) and a digital-to-analog converter (DAC). Your older DVD player contained both of those, and most receivers these days will also have those. To stick with your current receiver and DVD player, you'd need to get an external processor. Outboard processors are a niche market, and I honestly don't think it's worth looking into. A new receiver or different DVD player will be less expensive unless you find a used outboard processor. I've seen them for about $100, but I'd suggest using that money to get a new receiver. For around $250, you can get into most of the latest processing and connections (such as HDMI).
BTW, which new DVD player did you get?