A model number may help others help you.

[COLOR="Blue"]Bought a new heater and the two thermostats that go on the side of the heater.[/COLOR]
Did you check any of these parts to see what was blown?

[COLOR="Blue"]Do I have defective parts from Appliance Parts Pro,[/COLOR]
Always a possibility that a part is bad directly from the manufacturer.
Always a good idea to check parts before installing them.
Though they did work OK when installed so odds are that whatever caused the unit to fail originally has done it again.
Could also be that a replacement part has failed prematurely.

[COLOR="Blue"]or could the other two thermostats be bad that I didn't replace?[/COLOR]
The 2 thermostats on the heater are usually the heater's thermal fuse and the high limit thermostat.
They usually recommend replacing both as the hi-limit should have regulated the temperature so that the thermal fuse did not blow.
There are other conditions which can blow the thermal fuse but usually this is fixed by replacing the heating element which you have done.
The 2 thermostats on the blower are usually the motor's thermal fuse and the cycling thermostat. Could be the cycling thermostat but again the hi-limit should have prevented the heater's themal fuse from blowing.

[COLOR="Blue"]Would I be correct in checking the heater again with an Ohm meter, would I get a signal across the 2 leads of the heater if it is good as well as the two therrmostats.[/COLOR]
Yes
I would not assume anything.
I would start by checking power to the unit.

Try flipping the breaker off/on slowly a couple times, sometimes you can loose half the line without actually tripping the breaker.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
[COLOR="Red"]Be careful as 240 volts is lethal !!! [/COLOR]

Then check the heater, thermostats and fuses.
If the heater fuse is blown you will have to determine what caused it to go.
Note: that sometimes they do just blow on their own but changing it without checking other things is a gamble. I beleive richappy (another regular poster on this forum) has done a study on thermostats and found a wide variation of actual trip point and what is specified.

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate it.

If the above is OK then you will also have to replace the hi-limit as it should have regulated the temperature so the fuse did not blow.

You still have to find out why it blew.
Check that the belt is OK.
Check the seals (drum etc) in the unit. The air is pulled over the heating coils, through the drum and pushed out the exhaust. So any large seal leak will pull in room air and the cycling thermostat on the blower will run the unit hot.
Check that the lint filter is not coated with fabric softener residue which greatly reduces air flow.
Check/clean your vent system.
Check/clean the blower wheel.

If all OK you may want to replace the cycling thermostat as it's contacts may not be opening (welded shut).