Rebuilding NiCd battery cell packs can be a good alternative to buying new packs. There are really only a few manufactures of these type of cells, but the quality can differ as the prices may indicate. The majority of the price of a new pack is the pack package itself, which is specific to each tool, even though the cells inside are pretty similar. The amp hour rating and number of recharges it will take are the most important thing. I have noticed that the Porter Cable battery packs are a lot less expensive than most of the other brands. To be honest, I haven't researched the brand of cells they use as an OEM, but you can get info online about cell manufacturers and ratings on the quality levels. I would look closely at the warranty the rebuilder is offering, which cells they are using and avoid a bargain basement price with a poor warranty or hidden costs such as a "recycling fee". A supper low price on a rebuild or a complete replacement may indicate a clearance of old stock. NiCd's hate to sit around for long periods uncharged, which can really affect performance and charging ability. Check the date codes and don't accept any that may be much over 6 to 9 months old.
You can buy LED fixtures off the shelf, which are basically ready to go. I've seen these as puck-shaped lights that are basically designed for under-cabinet or shelf lights.
![enter image description here](https://i.stack.imgur.com/5b8We.jpg)
There are other pretty simple off-the-shelf solutions as well, such as using rope light.
If you are talking about using raw LEDs and literally doing everything yourself, it's pretty simple. You need to get some high output LEDs (pay attention to color temperature, beam angle, etc to make sure it is suitable). You can get LEDs in different packaging: clear/diffused, large/small, forward/side-emitting. Likely your best bet will be a large frosted one. How many you need will just depend on how much area you're covering, and how bright you want it.
![enter image description here](https://i.stack.imgur.com/GiGvM.jpg)
You'll need a DC power supply. The exact values are all dependent on what you use, so it's very hard to give an answer here. There are online LED array calculators available, which can give you something like this:
![enter image description here](https://i.stack.imgur.com/g8vMn.png)
One of the major disadvantages of serial wiring (shown here) is that if one LED is disconnected or burns out, they all go out. Finding which one is broken can be difficult, and if you've ever done this with x-mas lights you'll understand what I mean.
Another possible disadvantage of the DIY solution is that you are either going to have to come up with a nice way to package this all underneath, or you'll have a bunch of wires and bare LEDs hanging under your cabinets (maybe hidden by some moulding, but still). This may turn off future potential buyers. Off the top of my head, using some split-loom tubing may be a way to hide the wires and make it look at least half-decent.
![enter image description here](https://i.stack.imgur.com/fRC6V.jpg)
Best Answer
Almost certainly not. Virtually all inverters are set up for 12/24/48V input, none of which you are going to get from stacking 18V batteries. Even if you did find one suited for the odd voltage input, the capacity of portable power tool batteries will quickly be exhausted, even if you have "a few" - and paralleling those few can cause problems with the batteries - the weakest one gets lower than the others and the others try to charge it - depending where the battery protection circuitry is, you either kill the battery as the internal protection goes off, or you get battery flambe (likely just the boring dead case with a major brand like Makita.)