This subject is a total pickler mate, I spent an hour soldering new components on to mine and it is still the same.
I have a couple of questions, maybe we can narrow it down to something before you go forking out.
1 - Is the immobiliser light still flashing or stuck on solid; or not on at all?
2 - What does the immob. light do when you turn the ignition on?
If the immobiliser light is on solid and the remote central locking doesn't work, go into the fusebox and remove the fuse for the dash display, turn the sidelights on, then replace the fuse.
If the immobiliser light is flashing rapid when you switch the ignition on then I don't know a possible cause as mine does this and the display eventually powers up after maybe 10 or so miles/minutes, this is why I have been at mine with a soldering iron.
If it doesn't light up at all, not even the immobiliser light then double check the display fuse and all the other fuses in the fusebox, compare them against the ratings listed in your owners manual to make sure they all have the correct rated fuses while you are in there.
Beyond this, it is possible to remove the dashboard top on the espace (easy to do on a mark 3 ('97-'03)
it may be worth removing the unit yourself and checking the connectors and bulbs.
A last resort would be to try replacing the diode on the displays circuit board yourself, if you can solder then it's a fairly simple job and the replacement diode is about 40p.
Diodes tend to either work or don't, if it fails it stops and that's that.
I don't recommend doing this until Renault have told you it needs something else at a far higher cost as replacing it is expensive if you screw up here.
In the end, it may be a fuse blown due to water leak into the interior causing a short or something to drain the battery so I can only call what I've told you speculation
, it is by no means a definitive answer for the problem.
It does however give you a couple of things to check before you shell out, with a large slice of luck it will turn out to be a fuse.
If it really is screwed, it seems the dash repair place is the best and most economical bet, I think they're known as BBA- Reman, I reckon there will be other places that will do it too so best to shop around or get a recommend from someone on here who's had a display repaired.
Hope all this helps somehow.