Your Blu-ray player may or may not have the capability of playing Region 1 DVDs, but I know that mine, a Sony Blu-ray, will not play Region 1 DVDs.
I've had to hang onto my old DVD player just to play the American DVDs I have, because I was able to "hack" it for region free playing -- you find a code on the internet, enter it using your remote control according to instructions, and it simply reprograms the machine to accept all regions of discs. .
However, that's only for plain old DVD players, and I'm not sure Blu-ray players can be changed the same way. There are Blu-ray players that already come region free not just for Blu-ray discs but for DVDs too; you might be lucky enough to have one of those, but if not you'll need a DVD player for it.
If you don't still have your old one, the upside is that DVD players are quite cheap now that Blu-ray is starting to dominate the market.