Im pretty sure all the problems with Sega happend way before the Dreamcast was ever produced.
I say this because, what if Tom Kalinske was still head of Sega of America during the Saturn and Dreamcast days, and if Hayao Nakayama wasnt in charge of Sega of Japan or his desision of letting Kalinske go never hit his skull, Sega would be in the market today.
http://www.sega-16.com/feature_page.php?id=245&title=Tom Kalinske: American Samurai
If your done reading this, your probably thinking how Kalinske is pretty sweet guy and made Sega the powerhouse bomb during the early 90's. If Kalinske was still around by the time during the Saturn life time and well heck, during the Dreamcast, Sega would still be the house hold name like Nintendo is today. Sure, the Dreamcast would have a tough time competeing with Microsoft and Sony along with Nintendo, but with the right people, it would be on top or near it.
Sega made alot of stupid mistakes in the past, killing off the Genesis to early to rush the highly failed 32x, then to rush the Saturn, only to have a SoA president Bernie Stolar at the time wanting to kill off the Saturn to make way for the Dreamcast immedietly when sales were down. The Saturn had much potential, but like Sega, they did very stupid stuff. Cancelling the only Sonic game for that system Sonic Xtreame and having a president who wanted nothing to do with RPG games and had bitterness against Working Designs, who has made alot of jems for that system, it wasnt a pretty picutre.
After watching the video that TheReaper01 posted, it seems Stolar was really trying to get Sega back on track. Even though alot of Sega fans disagreed with what he did with the Saturn, if the system wasnt selling like it should, then what else can you do with it.
According to the vid, Sony really did give Sega a blow by launching the Playstation 2, and making it compatible with DVD, something im sure if Sega knew about earlier, they would add that to the Dreamcast. But if you did that, Sony would definetly know of Sega espianoge and take Sega to court, so its something Sega didnt need.
So, the Dreamcast exsist it seems for Sony and Microsoft to make a stepstone onto their success.
Its kinda funny, the Dreamcast failure seems to outline what Sega is today...