Are you saying that they charge you for $725 for the motherboard, and then they will start looking at your monitor problem. So the total cost of repairing will be $725 + X ?
I assume you DO NOT have access to another T42, which you could tear apart and do some experiment. Otherwise, it's pretty easy to identify if it's the inverter problem or not.
---------- Option 1: if you are very handy and want to try -----------
The first thing I would try is the backlight first.
http://www.ecnmag.com/article/CA414994.html
In my opinion, the chances for the backlight (small Fluorescent lamps) to break due to the drop is much higher than LCD inverter. The lamp costs abotu $70 + shipping.
Of course, you need to take apart you Laptop LCD and do some soldiering.
If it doesn't work, it could be the inverter. The just go to eBay, search for "T42 inverter", and you will find an LCD inverter for about $38 + shippping.
---------- Option 2: if you are not very handy or you don't have time
Go to eBay and search for "T42 LCD". Make sure you bought the SXGA one or XGA depending one what's currently in your T42. This costs about $300.
If it doesn't work, buy an LCD inverter, and at the same time, sell the LCD on eBay.
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Again, all the above is based on my guess of "lamp breaks easier than inverter". If you still think you want to try inverter first, go buy an inverter before you try a new LCD or a new lamp.