We repair LCD displays all the time. But, they ARE able to be separated (B/L and LCD). It could also be your inverter
(feeds your B/L). The B/L assembly consists of a cold cathod light "bulb" (sort of like a flouresent tube), a light pipe (causing light to be fairly uniform over the whole screen
area), possibly a BE Film (Brightness Enhancement - causes light to be directed toward the LCD rather than scattering about), and one or more defusers (used to make sure of uniformity of light). And, in most cases, as I mentioned, an inverter
Those items typically make up a backlight assembly. Unless you are an LCD repair center, the parts
will not be available. The LCD manufacturer (not the computer maker) will typically keep a supply of parts. But, after a few years, they will let the stock run out and will not repair the older ones (it just isn't cost effective for them, or for the consumer).
There is no phosporous panel (usually - who knows in their system) since nothing electrical
is connected to the backlight parts OTHER than the bulb, I have no idea why they would say it is soldered in (unless their manufacturing process solders a frame around the B/L assy. and the LCD for ruggedness). Alignment is important - we do it everyday without "special tooling".
You didn't say how old your unit is. If it IS 7 to 10 years old, hell they may have used phosphorous panels
???? Certainly isn't today's standard method. The price
for the unit then was probably pretty steep - the price
to repair the LCD B/L isn't that much in comparison. The problem from YOUR point of view would be that you can buy the "same" computer NOW, for about 1/4 of what you spent 7 to 10 years ago; and if you look at repair / replacement of the B/L assy from the current
pricing, it might seem a bit steep.
Hope this has been helpful.