Well "region free" really has nothing to do as to whether a disc is in NTSC or PAL. Region coding and NTSC/PAL are two different things.
Region 2 DVDs for example can be NTSC or PAL.
It sounds to me as if you've taken the region coding off some PAL DVDs and they played on your old system. They're still PAL, they haven't been converted to NTSC. They're just no longer locked to any region.
Most DVD players will play any region free DVD regardless of whether it's PAL or NTSC but - this sounds like your problem - your new TV may be set to recognise only NTSC and will not recgonise the PAL signal coming from the PAL disc.
Check the instruction manual that came with your TV - there is usually a way you can switch the TV settings back and forth between PAL and NTSC. Some TVs do this automatically, some need to be set by the user each time. Check the setup sub-menus on the TV if it's not in the manual.
It's unlikely with a modern DVD player but you may also have to set the output of your DVD player to do the same (it may need to be told it's now broadcasting to a PAL TV and not an NTSC TV). Again, check the instruction manual.
Hopefully you'll only have adjust one of the two devices - TV or DVD player - each time and not both. Just experiment and see what works.
I've had heaps of friends in the USA who complain they can't import and play PAL discs from overseas because their TV/DVD setup is NTSC. Most find it's a problem easily fixed when they find the PAL/NTSC switch listed in the instruction manual.
Hope this helps. Apologies if I've misunderstood your problem and am unintentionally speaking down to you about something you already understand.
If that doesn't work your other option is to actually convert those PAL DVDs to NTSC. That's a slightly more complicated and lengthy process to do as you need to run them through a video editing program and convert the frame rates. Its not impossible and there are free programs out there that will give you a decent conversion but it won't look as good as the original. It can also take the computer ages as it has to work through everything frame by frame.