It mostly depends on the style of the old cabinets. If they are full frameless, they may be fairly easy to adapt, but if they are full inset, they would be more difficult. Will the old style blend with the new? If so, and you are able to find a cabinetmaker who can adapt them for you, go for it! But, it may be just as costly to adapt as to have new.

If you had them "rebuilt" and it didn't work in your reno, is there somewhere else you could use them? Perhaps in the garage or basement.

Oh, one can always find a use for old cabinets! My first thought was to throw them on Craigslist.

Can you explain the difference between full frameless and full inset?

Complete waste of paid labor. If you can't DIY then donate them.

I found homes for every one of my old kitchen cabinets. 48" uppers and base in the laundry room where I used to have ugly metal shelves (love having that folding space!); a bunch of uppers in the garage where I used to have open shelves (now my garage stuff won't get so dusty); a small drawer stack and the diagonal corner cabs went to my neighbor's garage; a final upper cabinet went to the other neighbor's laundry room. The only things I actually threw away were the crappy lazy susan cabs, and the sink base (which I had to tear apart to remove).

I agree with hollysprings - trying to make the old ones fit might be a lot more trouble than it's worth, but 12" cabs in the garage work just fine for washer fluid and lawn mower oil.

Our electrician asked if he could have our old cabinets, and we were happy to give them away - any repurposing is good but we don't have a garage.