I'm not familiar with this printer; all I've done is read some of the online documentation. I suggest that you use Google to search for Epson Printer Repair in your area and take the machine in for service.
The service manual for the Epson Stylus RX420 is here --> http://diagramas.diagramasde.com/impresoras/EPSON%20Stylus%20Photo%20RX420-RX425-RX430.pdf
According to that manual, your control panel looks like this:

There are (at least) 7 lights on this panel and a "7-segment LED" display which is where you might see an "E" if there is a serious error. From your description, I believe the "Power LED" (the green light) is flashing and the "Error LED" (the red light)
is on (but not flashing). The manual does not describe any condition that results in this pattern (see pages 49-52 of the pdf manual linked above).
If in addition to the power light flashing and the error light on, all of the other lights were flashing and an "E" was flashing in the 7-segment display, that would indicate a "maintenance request" because the overflow sponge is full. That's typically
a job performed by a repair shop, but a handy user can do it as well. However, that's not the situation that you've described.
Sorry I can't be of further help.