Welcome to the forum!
Congrats on the new receiver. I have two Pioneer's and really like them. What you are wanting to do isn't all that uncommon, but there are a some things other than physical connectors to consider. Before I get into it, I'll summarize my thoughts - you can do it, but you'll likely be better off spending some money on some new speakers. Now, for the specifics.
First, you can connect the speakers to the receiver with the exception of the subwoofer. The connector on each speaker wire that connects to the Philips receiver has two wires that go into it - those are the two wires that you'd be connecting to the speaker terminals (black and red) on the back of the Pioneer. You can either cut off the connectors, or you could use extra wire that would go between the Pioneer's speaker terminals and the connector on the end of the speaker wire. Those are some options, and we'll be happy to help you with the details if you want/need that.
Now, for the other considerations. Those speakers are rated at 3 Ohms nominal for the front and rear speakers, and 6 Ohms nominal for the center speaker. The Pioneer won't have any trouble with the center channel, but the front and rear speakers have a lower impedance than that which Pioneer guarantees will work with the 1019. A lower impedance leads to a higher current draw form the amplifiers in the 1019. This probably won't be a problem if you listen to your music/movies at lower volumes, but if you like to crank it, the 1019 might go into a protection mode because the current draw was too high.
Also, the 1019 can't power that passive subwoofer that came with the Philips system. The 1019 has a low-level output for a subwoofer that is intended to be connected to a powered sub (a sub with an amplifier of it's own). I believe that we can make that work for you by using the Philips receiver as the subwoofer amplifier, which just means that you'll need to have the Philips receiver on, as well.
Again, we can help you get this set-up and working. I just wanted to present some information to help you decide if you want to pursue this particular approach.