This "trying to shift" problem is usually an indication that the cable needs to be adjusted or excess friction in the cable housing. You can try adjusting the cable at the barrel adjuster. If that doesn't work you probably need new shift cables and cable housings. The short housing found just before the rear derailleur often becomes dirty from picking up dust and dirty spray off the road.
www.parktool.com has good instructions for cable and derailleur adjustments.