Errors 2F00:0B1C and 2F2F:0119 (System Memory)

I have an Inspirion 1100 Notebook that is a little over 3 years old.  When logging into Windows XP, it unsuccessfully returns back to the login page.

 

I ran the Dell Diagnostics CD.  I received had these errors:

 

2F00:0B1C = Memory data data bus stress test failure

 

2F2F:0119 = System memory failure.  Read 00000040h, expected 00000000h at address 05E19050h.  Suspected memory component located on System board at label DIMM_A.

 

I have two 128MB RAM memory sticks.  I took each out and placed them one at a time in the DIMM_A and DIMM_B slots.  I re-booted each time and had the same behavior of not being able to log into Windows.  I think this tells me that both memory sticks are bad, but am not certain.  Perhaps I need a new motherboard?  I am not experienced enough in this area to diagnose the exact problem.  I appreciate your assistance.