I bought them but I haven't tried them yet... Next month I'm going to test them with my application...

I don't know if 4.24 volts is fine, maximum is 4.20 according to the manual, just in case to test, add a diode to reduce it a little.

A few questions to rule things out:

1) Are you enabling them? (pin 5 active low)
2) Are you using a 1k resistor between the PIC and RX (pin 3)?

That's all right now, it's 6:30 in the morning and I'm going to bed...