Whats with the third party matters in a console success???

[Tetsuya]

im really a little kind of fustrated over the fact that third party sells consoles is that true??? did the following consoles have third party support....just answer yes and no k???

Nintendo 64

Sony Playstation

Sega Dreamcast

Sega Saturn

Nintendo Gamecube

Sony Playstation 2

Microsoft Xbox

Nintendo DS

Sony PSP (IMO it has alot of third party support but isnt selling well)

Microsoft Xbox 360

Sony Playstation 3

Nintendo Wii

so what everyone is telling me is that if many and many third party developers support a system it will sell well???

is it like this

System sells = third party support or having good connections with third parties

or

Third party support = good selling system

am i right or wrong???

please help me out!!!