It depends on how the old DVD's audio connected to the surround system. 5.1 and 7.1 analog outs went away from Blu-Ray players built after Feb 2012 because the Hollywood studios wanted that and mandatory Cinavia copy protection. They disappeared from DVD players around that time too because those became too cheap to include such premium features.
If the old DVD player connected via digital: coaxial or optical S/PDIF, then nothing has changed.
If it's an all-in-one system where everything is in one box then all connections are internal and it's junk now.
It depends on the new system, If it include HDMI connector then you can use the HDMI cable, otherwise you can use the same old RCA cable to connect.
If you can post the link of your surround system as well as your new DVD player, then it will be much easier to tell.
This is a dead giveaway for one of those all-in-1, all integrated boxes, that is not expandable and can't hookup anything else to it. As mentioned by others, look for an HDMI IN (IN for input important) connector in the back of this system. If absence then can't plug in external DVD.
Just to keep your hopes alive, the presence of a COMPONENT IN connection (5 RCA cables) and an Optical IN may substitute for the HDMI, as long as, the external DVD does also have these connectors.