Sorry to hear of any continuing issue with registering the handset(s) to the main base of this system.
Let me be absolutely honest with you about these RCA phone systems. Over the years, these systems used to be "pretty good" - especially when purchased as part of a "single package" - where the handsets were already registered to the main base - at the factory. But in more recent years, these systems have "gone down" in "quality & reliability", along with the ability to even purchase a multi-handset system. My personal belief is that this brand has "backed off" in the making and support of these phones - to concentrate on other products and/or to reduce the cost of these systems.
On the other hand, there are OTHER brands that have done an EXCELLENT job of continuing to make and support relatively inexpensive 2-line phones - with cordless handsets. The most reliable brand I have seen over the last several years is Panasonic, and they make a 2-line system that actually comes with the handsets already pre-registered - in the same package. Plus is is relatively EASY to register AND de-register any additional handsets you may want to purchase for the system.
Since you purchased this system from Amazon, what I would really recommend is trying to RETURN this system (and additional handset) for CREDIT towards the purchase of a Panasonic system. I have a link below that appears to be almost an EXACT REPLACEMENT for the RCA system, and from what I can tell, may be just about the same amount you paid for the RCA system.
Click Link (below) for 2-line Panasonic cordless phone system
From what I can tell, this appears to be a "Sold by Amazon" item, and prime eligible, so you may be able to get it within a day or two, and have a working system (once the handsets are charged).
Please let me know what you think, or if you have any more questions.
Thanks, ***** *****