@TyePhoid,
Quite simply we know that it is the gaming division specifically that is causing Sony to lose money right now. Now looking at the gaming division there are currently three major products of interest.
Those major products are the PS3, PSP, and PS2. So of these products we are extremely confident that the PSP and PS2 are both profitable on hardware and software. This leaves the logical and very easy conclusion to be made that the large loss in money is from either PS3 hardware or software. Given the history of software and the apparent cost and production problems with the PS3 hardware I think it is beyond clear to see that the PS3 hardware is the source of these losses.
Hopefully that should put your questions of "how do we know" to rest.
Now as for how they are doing as a company, I will say that anyone who tries to insist that they are broke is deluding themselves. Sony has quite a bit of money still, the problem however is that they are having a hard time justifying the continued spending on loss leader strategies for the PS3 when it is the only source of significant losses for the company. Stock Holders and directors can tolerate this for 2 or 3 quarters but realizing that the high cost to develop the PS3 was being felt far before the console was released you can see how this has been a constant for the company for probably 2 to 3 years now.
I will reiterate myself once again, they are not going out of business. Its not going to happen. But it is possible that they decide to stop with their loss leader strategy and take up a damage control strategy and attempt to salvage face and hopefully recoup some or all of their investment. In short, I think it would be naive to think that Sony is not displeased with the PS3's performance and it would be extremely naive to believe that they haven't put together contingency plans to stop the bleeding when/if necessary.
Finally, some folks are going to screech at the thought of this post, but the fact is that they are likely unable to distinguish the difference between someone saying the console is bad in a business sense and saying it is bad in a recreational sense. I am only saying that the PS3 is bad in the business sense.