Hi, I have a few things for you to try.
1. Your TV "6424TF" seems to have problems with its IR "Infra-red" sensor going bad. This is a common problem with your model TV. If this is the case no remotes will work on your TV.
2. Because I do not know the model of your universal RCA remote I cannot tell you how to program it.. please supply the model number of it. Try looking under the battery cover. might be an "RCR..." number. I need to know this because all universal remotes have different codes and programming methods.
3. To know 100% if its your TV that's bad you will need the original remote for your TV. I have already looked up your original remote and you can purchase a brand new replacement that will work right out of the package (assuming your TV IR sensor isn't broke) here: RR0108UD for all sylvania TVs
. no programming is necessary for this remote.