If after all your attempts above and colourful vocabulary utterings it still won't move, try using a hammerdrill with a good screwdriver bit, the pulsating might loosen it. If that fails drill a 1/8"th hole right in the middle about 2" deep, then try again, there should be enough of the slot left to fit a large screwdriverhead. If still no joy, next a 3/16"th hole etc. You may need to use a thicker screw when replacing the box.
Try tightening them slightly first. This is an old trick to break the grip of a rusty screw on wood and can allow removal. But do as Eddie says - use a close-fitting screwdriver blade.
thanx for help - the screwy bits are jammed into the old metal plate and they dont have slots for screwdrivers; I've tried pliers (not the singer) with T cloth for grip & WD40, hammer, brick & dogs teeth to no avail. The replacement hasn't got any screwys - that's why I need the old ones. Drills will make them un-usable.
Expect I'll have to wait for a handyman - by which time I'll have forgotten where the bits are.....Oh for a man about the house ;)
If you can grip the end with pliers then it is probably as docspoc first spotted, you have bolts (and nuts on the other end which are probably covered to protect your hand). You need spanner(s).
Invite the chap from nextdoor over for a cuppatea and ask him innocently if he knows anyone who can renew a letterbox. He will have to be a pretty crude neanderthal not to offer to do that little job for you.
The screws are fitted into the letter plate, before the plate is fitted to the door.
It's actualy quite difficult to drill the 2 screwholes at exactly the same angles..so when the plate is offered up to the door with the screws attached ...you normally find that the plate has to be forced into the door, while trying to keep the screws parallel...usually it jams. You will have exactly the same problem when trying to remove it...it's already jammed.
If you cant get the screws to turn with a pair of mole grips...hammer them out..!
As Rov said,,get a large screwdriver and hammer it into the corner of the back of the letter plate.Do this to one side and then to the other just a bit at a time...It will come out..
Promise..!
As a rule.. new screws are supplied with the new plate...but if not. have a look where you bought the plate..they should be available in pairs, along with the domed nuts.