Telephone wiring question
First of all, you don't need special telephone wire. You can use the same wire you use for networking - e.g., Cat 5, Cat 5e, etc. I used to use leftover old Cat 3 for telephone wiring, but once I went through all that, I switched to using Cat 5 for everything even if it costs a little extra for the phone wiring than absolutely necessary.

Telephone wiring does have polarity - i.e., red/green is different from green/red. But it does NOT usually matter.

The middle pair on T568A/B wiring is the same as the pair (aka red/green) for standard phone wiring. You should use RJ11 (1 pair = 1 phone line) or RJ14 (2 pair = 2 phone lines), but you can actually use RJ45 network jacks and just connect a pair to pins 4/5 for one phone line, though the patch cables may not hold as well as with RJ11/RJ12.

Troubleshooting:
Ideally you should have three tools to test:


A telephone test set. But for very occasional use, you can simply use a phone - preferably a phone that does not require any power beyond that supplied by the phone line. Plug it in at each point that you need to test, and if you get a dial and can make a call then you are good, and if you can't then you need to keep working on it.
A tone generator/detector. Mainly for checking when you are trying to figure out which cable is connected to which port. Keep in mind that there can be false positives - i.e., it is good for figuring out which cable is which, but not so useful for figuring out which pair is which.
A wiring tester. This one is just a random example - there are many different types but basically something that lets you put a remote on one end and a master on the other and see which wires are connected correctly, reversed or not connected. This is extremely useful for Ethernet cabling, but helps with phone cabling too.


Just work through it step-by-step. First check the Comcast modem and make sure a phone (or test set) works there. Then put in the splitter and make sure each connection works there. Then put in the next patch cable and check there, then the long cable run to another room, then its patch cable, etc. At each step if you can't see the problem then use the wiring tester to see what, if any, wires are actually connected.

I also recommend NOT using a long cable with plugs on the ends. Wire up (same for Ethernet) jacks on each end and use short, easily/cheaply replaceable, pre-made patch cables for jack-phone, jack-splitter, etc. Properly installed jacks rarely go bad, but plugs on the end of long cables often go bad.