If that set still works, you might be able to put it to good use as a second set in a bedroom, den, etc. Hitch a converter box and an antenna to it and it should work just fine. I had (still have) an RCA 19" TV from about 1999 or 2000 that still works (the antenna connector broke after the first six months,
but the set has worked great ever since), although I put it in my bedroom when I got a flat screen some years later.
RCA televisions didn't have serious problems (to the best of my knowledge and belief, anyhow) until Thomson bought them out in the '90s. At the start of the decade, they started using an onboard tuner design that, as the name implies, soldered the RF tuner directly to the TV's main PC board. These tuners often developed cold solder joints at the ground points around the tuner shield; this often caused noise to enter the "jungle" IC (a chip with many leads that practically ran almost the entire set, since it contained much of the TV's circuitry) and eventually destroyed said IC.
RCA (Thomson) eventually got enough often bitter complaints about the problems caused by the onboard tuner that they finally started mounting the tuner remotely from the main board; this first appeared in the CTC203 chassis and has been used in every RCA CRT set since. It wouldn't surprise me if they used the same tuner mounting scheme on their flat screen sets, although I have been reading lately that "RCA" branded flat screens are very bad news when it comes to reliability; that is, the tuner may not cause any problems in these sets, but other problems related to cheap parts, etc. just might send these sets to the landfill (after the warranty expires) sooner rather than later. I personally would never own a late-model "RCA" flat screen television for just that reason.