Installing iPod Touch 2nd Generation Logic Board in iPod Touch 1st Generation Casing

Ok so I was thinking if this was entirely possible while I was fixing my old 1st generation ipod touch.

I took apart my iPod touch 1st Generation 8GB because the home button was stuck (jammed in and even the clean it out with a cotton swab didn't work).

While I was fixing that... I made a clumsy mistake (due to how hard it was to take it apart... thanks to the adhesives) and accidentally broke a part of the logic board (more like quite stupid mistake on my part for handling it from a corner instead of holding it by the entire base itself).

I was wondering... is it possible for me to purchase the iPod touch 2nd generation (or hell maybe even the 3rd Generation) Logic Board and the other extra items I might need and just install them into the iPod touch 1st Generation casing (including using the iPod 1st Generation's LCD screen). Using the same iPod 1st Generation battery wouldn't be that bad either (Although I don't know if they use the same batter or not as... well... I haven't done too much research into the backgrounds of the 3rd generation logic boards and essentially taking them apart).

I was thinking... because logic boards cost less than actually buying a new ipod (especially if they are interchangeable... which actually might not work).

Anyways... Yeah...

Edit:
of course I forgot to mention... If I would attempt with the 3rd generation logic board... I would need to upgrade the hard drive right? Especially since 3rd Generation doesn't seem to have 8 GB iPod touches