So my laptop (same one I've been trying to get a mouse to work on) had a blank screen, at all times. I can vaguely see the desktop or whatever is shown by using a flashlight, but I'm confused whether this requires a new backlight, or simply a new inverter.

I've already found the thread concerning opening up around the screen to view the FRU and PIN numbers for my current inverter (FRU: 27K9951 EC, PIN: 27K9952, on an IBM ThinkPad R51), but I'm unsure where to go form here. After a few Goole searches I've found a few decent prices (best being around $50) for an inverter, but I want to be sure I'm buying the right part to fix my problem. Just some confirmation or helpful tips would be helpful from the community, thanks a bunch.

P.S. I have already found the thread with the pictures of removing the frame, and from it I've understood that it is the inverter I need to replace, but better safe than sorry, I suppose - don't want to buy a $50+ part I don't need.

Inverter.
That is a very high price for an inverter for an R51, but the R51 is a very rare computer... so you may have to pay it.
you need a very good quality #1 hard steel philips screw driver, great care in removing and replacing the screw covers, and the time it takes to remove and replace 18 screws. But the inverter just plugs in. Mark all your screws as you remove them as they are not all the same length or diameter. But the most important function is removing the screw hole covers so you can use them again. You will benefit from a very, very thin flat blade screw driver or other tool to lift the screw covers out and off. You will need a nice adhesive that remains soft when you replace them.
It is very rare for an inverter to go out in that model.

Ya, I've already pulled off the frame, and removed the old inverter. I'll have to order one in the morning, but I'll be digging for competitive prices, thanks though.

Ok, so in the picture on where to find the FRU number for the Inverter, their FRU and their PIN are the same, whereas my part listed 2 separate numbers.

With this page it lists an inverter "Board" and an Inverter "Card" separately, one with my PIN and one with my FRU. They are the same price (only $29.99), and they happen to have the same quantity, so I am wondering if it just covered the bases by posting this thing twice?

I just need a quick point to which part I should be buying, thanks - again, my specs for the Inverter were (FRU: 27K9951 EC, PIN: 27K9952, Hitachi INVC648, on an IBM ThinkPad R51)

EIDT: Crap, meant to edit the last one and ended up double-posting, sorry.