(1) The Cmos battery would not normally cause a screen problem. Indications of cmos battery fail - (1) Time and date get reset or (2) an error message when you boot.
(2) Three possibilities. (A) A connection in your desktop has become loose, so reseat all cards (ie graphics card and Memory) and MB connectors. (B) you drained the cmos battery. CMOS batteries are a VERY low current drain battery and can be drained easily - replace battery. (C) Worst case, you damaged your MB or corrupted the CMOS (AND YES as zalittle indicated, they could be a resualt of ESD) - Both of these probably will require replacing your MB.
(3) My recommended steps :
.. Do 2(A) - still no work
.. Replace battery and while the battery is out you should have two pins labled reset or clear CMOS, short these pins for 10 Sec (With Battery OUT).
Still no work - look at Troubleshooting guide, it provide some very good steps - then come back