I have wired my phone from our cable modem to the phone junction box for our home in the basement. I stripped and hooked each of 4 teeny tiny delicate wires to the junction box. For the most part this works, but I'm wondering electrically what I could have done that would cause me to be able to hear the people on the other end--but prevent them from hearing 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.
I think it's unlikely that your wiring is the problem. A single phone line is only two conductors, even though the connector has four contacts. The four contacts are there so that a single cord can support a two-line phone -- normally the two inner conductors are "line 1" and, if connected at all, the two outer conductors are "line 2". If one of the two conductors isn't connected, the phone doesn't work at all -- it's not like there's a separate wire for outgoing audio and another for incoming. I'm not saying it's impossible your wiring is the culprit, as I'm not an expert on phone systems and there may be some condition I'm not thinking of that could cause this, but I do think it's unlikely.
At any rate you can check your wiring job by plugging a wired phone into the phone jack on your cable modem. If you see the same problem, then it's not your wiring that's causing it. Try another phone just to rule out the possibility that your phone's broken, then call your VOIP provider to see if there's any network troubleshooting they can do.