Can Typhlosion's "Afterburner" Poke-POWER be used if there is no Energy in the discard pile, just to place a damage counter on one of my Pokemon?
No. Since you can't attach an Energy from your discard pile to one of your Pokemon, you can't use the rest of the power.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)

Relevant cards

Note: All applicable cards may not be listed below.
HGSS1_110
HSP_HGSS09
HSP_HGSS09