Could we clone trilobites or other fossil invertebrates?

If we found dinosaur DNA in fossilized bones and could clone dinosaurs - any chance we could find trilobite DNA or anything from fossilized invertebrates? Seems they might be easier to start with, and I think they'd be way cool!!!!

First of all, I don't think there's any chance of cloning any invertebrate, extinct or not, from only the shell. So far as I know, invertebrate shells, even arthropod shells that are largely organic material (chitin, as opposed to clam shells that are made of calcium carbonate), contain no cells--unlike vertebrate bones. No cells, no DNA. So even if you could find a non-mineralized fossil arthropod (see below, about mineralization) you couldn't clone it.

Even if we restrict ourselves to vertebrate fossils, in principle this is going to be somewhat difficult. For one thing, isolating (or sequencing and then reproducing) DNA from an extinct organism is only the beginning; you then have to replace all the DNA from a cellular nucleus with your desired DNA while ensuring the nucleus remains viable, then transplant that nucleus into an egg cell.

Even if you say that we are able to do that (and we might, soon enough), you still have to get your DNA. Unfortunately, DNA is an extremely fragile molecule that degrades very quickly under normal, natural conditions. (That's why eukaryotic cells package the stuff in protein and enclose it in a membrane.) It's hard enough to get good DNA samples from 10-year-old bodies. The "blood sealed in amber" scenario from Jurassic Park is probably the most plausible way Michael Crichton could have found for his geneticists to get their raw material, but the fact is that--even if you could find a sample of 100-million-year-old blood and determine that it belonged to a dinosaur--the DNA would almost certainly be hopelessly degraded, simply by thermal processes. You probably couldn't get enough information from it to reconstruct any part of the genome.

And that's the best possible scenario. Most fossils that old (or, indeed, older than about a million years) are fully mineralized. That means that all the organic material (including DNA) has been chemically replaced with inorganic substances like limestone or silicates. This is a delicate process, too; the reason we mostly find ancient bones and shells is that these tissues were already partly or fully mineralized when the animal was still alive. So, while we were able to get some DNA from a roughly-100,000-year-old Neanderthal bone, there is no chance whatever that we can get it from a 70-million-year-old Triceratops bone.

That doesn't mean that more recent fossils can't be analyzed (like that Neanderthal) or even cloned. There's currently an effort underway to clone a frozen mammoth (or, failing that, to find viable frozen mammoth sperm to cross with a female elephant). Notice, though, that the mammoth fossil was frozen--not mineralized!