The object being edited/ in the 3D view requires transparency to be selected with <Z> or with the "limit selection to visible" button turned off before any vertices, edges or faces will select. It started in 2.58 or 2.59(don't remember). It is still there in 2.61 rev.42615.
The computer specs are
nvidia Geforce2 mx, petium 4 1.8ghz, 512 mb ram in a dell dimension 8200 windows xp