I guess that really depends on how many cells can you get? If there are over 500 cells, I probably use Qiagen Mini RNA Kit. If the number is low than that, you may want to take a look of the kit from NuGEN. They provide kit for extraction and amplification mRNA from even one cell.
There have been performed experiments from 1.000.000-5.000.000 cells. I see the pellet after centrifuge. I've also tried the Qiagen Mini, but i didn't receive any good result. I thing that the membrane of our cells cannot crushed, in order to release the RNA. I've tried proteinase K, as well TRITON X-100, or SDS, or other lysis buffers.
Do you use a cell line of stem cells? You really have a lot cells. Are they cultured stem cells or cells isolated from tissue? I know that when you culture stem cells, the sphere body will formed. So try to treat them with trypsin and separate them into single cell, which may help you with lysis. And you really don't need so many cells for RNA and you can use regular Qiagen Kit. Hope this will work for you.
To my knowledge, no cell can resist the chaotropic salts included in TRIZOL reagent.
Same for PK. Your problem is probably different.
Maybe you should use more TRIZOL (since, as Yugang Wang noticed, you have a lot of cells), to be sure to instantly inactivate all RNAses when resuspending your cells.
You may also be really quick when handling and resuspending cells, and work on ice, because RNA can also be degraded while in dying cells.
Finally and obviously, all your solutions, tips, tubes must be RNAse-free, and you should wear gloves since your skin is loaded with RNAses. (Sorry if I'm Dr Obvious there).