Could home phone wiring cause a one-sided phone call (where I can hear them but they can't hear me)?
One-way voice with VoIP is a networking issue, which is a bit off-topic for this site. This article may help: What causes one-way conversation in a VoIP network?. Unless you set up the voip accounts and hardware yourself (in which case you would have done things dealing with the acronyms SIP, RTP and/or NAT) then call your provider, because it's their problem. It sounds like you're getting service directly from your cable company, and frankly, if they can't get this right I'd be scared - that is not a good sign of the quality of service you'll get. 

What your cable modem has in it is called an Analog Telephone Adapter (ATA) - it basically interfaces an analog phone line with a VoIP account. Once you're on analog, both send and receive are on the same pair, and only a single pair of wires are used -- typically red and green (or blue and blue/white in Cat3+ cable). If these are connected, you have two-way voice between your analog phone and the ATA. If not, you get nothing at all. It's pretty easy to conclude that this is not a problem with your wiring.