As the flashing red light is now continuously on, I would suspect a fault may have developed. It would seem strange for it to be illuminated just because the battery is flat, indeed one would expect it to be off totally.
Agree a new battery is desirable BUT when ready to connect it, I would place an ammeter/multimeter between the battery terminal post and the connection cable to see if there is any excessively constant drain current. Otherwise, your new battery also might be flat in a few days!
Someone on here may be able to advise what a typical drain current is for your car, so that you have something to compare with.
