These cases are often held together with internal clips. The only telltale to where they are, short gaps at intervals along the join between the two halves of the shell. The idea is you insert a flat tool in the gap and this releases the clips -- in my experience frequently breaking them and scratching the case, so take care.
I have a Mitac in a similar state of half disassembly to yours and I'm waiting to find a second one as donor.
In the past, repairing older Dell Latitude laptops which were more obviously designed to be disassembled, I relied on having two similar models so that I could afford to wreck the case of the donor machine while learning how not to wreck the second one.