Dryer with one wire connected to water pipe does not work after replacing copper pipe with pex
Danger!
A 3-wire dryer connection has two hots &amp; neutral. It does not have a separate ground.
A 4-wire (required for all new installations for many years now) has two hots, neutral and ground.
The only time you should have a wire connected to copper pipe (and even then, it is limited for various reasons) is ground. Never neutral. So you appear to have two problems combined:

Neutral from dryer treated as ground by connecting to copper water pipe
Pex doesn't conduct so it is not a valid ground path

A typical US residential clothes dryer uses neutral for controls &amp; lights, possibly the motor. It does not use it for the main power draw - the heating element. As a result, it can &quot;kind of squeak by&quot; but in a dangerous way if instead of ground on neutral (the usual 3-wire way, now deprecated) you have neutral on ground. When you made the ground no longer work (because pex doesn't conduct), instead of just losing ground (a safety issue) you also lost neutral (a functional issue).
In a way, this is a blessing in disguise, because you have found a major safety issue before it had the chance to kill anyone (seriously!).
Get this Fixed Properly

Replace the 3-wire cord from the dryer with a 4-wire cord
Remove the jumper wire in the dryer that connects ground &amp; neutral (if you can't figure out how to do that, post the model # and we can probably figure it out)
Replace the 3-wire receptacle with a 4-wire NEMA 14-30:

The hard part: RUN A NEW 4-WIRE (2 HOT, 1 NEUTRAL, 1 GROUND) CABLE to your electrical panel. Normally this will be 10 AWG for 30 Amp. The problem is that based on what was previously done - routing neutral as ground - it is really not clear what you will find when you get to the electrical panel. I recommend posting a picture of the electrical panel showing the current dryer circuit breaker before doing any work so that we can review it for other possible issues.

In some cases if running a new cable is not a simple thing to do (e.g., different part of the house) there are ways to run ground separately through another path. However, that is dependent on ground being the only problem. In this case, all indications are that you only have 2 wires - not 3 - going back to the electrical panel, in which case taking care of ground through an alternate method will not solve the problem.