If the red light is flashing by itself, it means the printer thinks a cartridge is low on ink. Have a look at what the Status Monitor thinks (right click the printer Icon in the bottom Right-Hand corner and select Ink Monitor). This will show which cartridge it is. If it's the new colour cartridge, it means the cartridge is faulty (then replace it), or it is a refilled cartridge that hasn't had it's chip reset to "full". For this you will need a chip resetter, available on E-Bay very cheaply. If it's the black cartridge then replace it.
If both green and red lights are flashing, it usually means the Waste Ink Pads in your printer are saturated with ink and the waste ink "protection" counter has exceeded its limit. You can restore your printer to a working condition immediately by using the SSC utility - download from:http://www.ssclg.com/epsone.shtml
Install it, and double click the ssc printer icon in the bottom right corner (System Tray). Choose Configuration and set your printer type (C4x), then close the ssc window. Now right click the ssc icon in the sytem tray and choose Protection Counter. You should see that the current count is above the limit; then choose reset to set it to zero. You will need to fib about having changed the waste ink pads! Turn the printer off then back on again. This will stop the lights flashing and restore normal operation.
However, remember that eventually ink will overflow from the waste ink area and make a dreadful mess, so you must change the waste ink pads before this happens. This requires the disassembly of the printer.
If you decide to have a go at replacing the ink pads yourself, report back and I will provide further help. It is a pretty simple job once someone explains how to get the case apart!