I'm not familiar with the Parallax modules, but if they use the Linx LR series, then this receiver will output random noise even if the transmitter is powered down.

Look at the examples on dhoustons' website, and others he has posted here. He knows what he's doing.

You might also try a search here. I have posted several code examples for RF communications that are very simple to implement, and work quite well with PBP & noisy receivers.

It's just not that simple to get a reliable wireless connection up & going, and it's for sure not going to be anywhere near as simple as a 'wired connection', but there are enough threads here 'with code examples' that cover this if you look hard enough.