I just finished some repairs on my bike, (Mongoose 26" 21 speed). I noticed that for some reason when I try to shift using the shifter, it won't shift to the lower gears. I can't get past seven. I tried adjusting the H and L screws but that didn't seem to work either. I turned it upside down and had my sister pedal it while I used my fingers to shift it to 5, then 4, then 3, then 2 and then 1. When I stopped, the gear stayed in place while my sister pedaled. So I shifted back up and then tried again using the shifter, but it was stuck again. Is there anything I can do myself that wont require spending money at a shop?
You need to find out if the problem is with the shifter, cable or the derailleur
You have already ascertained that the derailleur it not jammed. Either, the cable is not pulling the derailleur or the shifter is not pulling the cable.
First, inspect the derailleur cable run from the shifter to the derailleur for any obvious problems such as the housing having come out of a stop, the cable having come loose from the derailleur, or the cable having snapped.
Bikes usually have a length of exposed cable on the top tube or downtube. Try pulling the cable away from the frame and see if it actuates the derailleur.
Undo the cable from the derailleur hold with pliers and apply some tension, actuate the shifter, make sure the shifter is pulling and releasing the cable.
You should be able to figure out where the problem is. It's likely a simple problem with the cable which is relatively easy to fix. Replacing the cable and housing is inexpensive and not hard to do. If the shifter is broken you will likely need the assistance of a bike repair shop.