Hello there and Welcome to FX-Sabers
The Luke SW205
wow this brings back memories
This is one of the original 6 cell battery packs so First you want to check the battery pack with a volt meter
to ensure you are getting power through the battery pack.
If not then you at least know the first thing to try is to either get a replacement battery pack or find
the broken connection inside the battery pack casing.
Hopefully it will just be something in the battery pack and you'll be able to get it up and running.
If it does have power going through the battery then it could be a problem in the hilt its self and at that point
you'll need to figure out how to get it open and I found a few links that may help.
Unfortunately the links are very old and the pictures no longer attached but you might be able to read through
them and gain some perspective on what you would need to do to disassemble it if needed.Luke ESB disassembly (complete, with lots of pictures) - page 1 - Data Sheets -Disassembly/Reassembly of Luke ESB
Now as far as is it worth it or not?
These old models are rather fragile inside and the sliding top button can be difficult to get off with out damaging it
because of the age of the plastic now as well.
No one makes a specific conversion kit for those anymore either so it would need to be a custom thing and the price
you were quoted doesn't sound far off for something like that and people have converted these over the years.
its just not something that people convert since actual graflexs are readily available now.Of course at that point you might just want to consider a better newer saber.
Good luck and again welcome to fx-sabers