As described, this is the default graphics device included on the motherboard 
of an eMachines T2824. According to the specifications at 
http://e4me.com/support/product_support.html?cat=Desktops&subcat=T%20Series&model=T2824
 , this is "IntelĀ® Extreme Graphics 3D / 64MB Shared memory".

The driver in use appears to be 'i915', based on the output from lsmod,
so...

Graphics card (per manufacturer): IntelĀ® Extreme Graphics 3D / 64MB Shared 
memory
Graphics card (per lspci): Intel Corporation 8245G/GL[Brookdale-G]/GE Chipset 
Integrated Graphics Device (rev 01)
Driver in use: i915

I have not tried any other login packages. Can you point me to some
instructions on installing and testing another package so I can give it
a try?

-- 
Ubuntu 9.04 gives black screen after splash, remote login shows hung/unkillable 
gdm instance
https://bugs.launchpad.net/bugs/370111
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