I was going to say RMA the laptop under Warranty but since you personally removed the screen the Warranty is voided if you still had one.
You should have taken it to a computer shop that specializes in Laptop repairs if you had no Warranty. But I understand why you wanted to do it yourself to save money since the repairs can cost almost as much as a new laptop.
Does the new LCD Screen work since you replaced it and just the back light is not working?
As for a the LCD Back Light not working it might not be a fuse. Do you have everything connected correctly when you assembled the laptop?
Could also be a damaged LCD Back Light assembly or the cable connecting the back light is damaged.
In the link below it shows how you can test the Back light once you have it disassembled to check it. If it has a plug you can check to see if it has voltage coming out of the plug which will indicate whether the lamp assembly is bad or damaged and just needs a new one.
If there is a fuse there would be two types, the regular tiny glass or opaque fuse or the solid state fuse located on the motherboard.