Your chlorine level is way too low for your CYA level. (Take a look at the Best Guess Chlorine Chart in my signature below.) I'm not sure how your pool store got a CYA reading of 120. The test actually can't differentiate values over 100. At any rate, you need to shock your pool up to 25ppm and try to hold it at that level to get rid of the algae. in your pool, each gallon (4 qts.) of 6% bleach will add about 4.8ppm of chlorine. Use that as a reference to help determine bleach doses needed.

Good decision to order the Taylor kit. You're going to need it in order to measure the high chlorine levels you're going to have to run. In the meantime until your kit arrives, you can use a dilution method to force your kit to read a little higher. It is not super accurate and is not meant as a replacement for the good kit but just something to use temporarily. Read about it here: Testing Without a Good Kit

Your pH is ok at 7.8 but if it goes any higher, you'll want to drop it a little with some muriatic acid. Be advised that pH readings aren't accurate at high chlorine levels. With most kits, you need to test pH when chlorine is no higher than 5ppm. With the K-2006, the pH reading should be accurate up to chlorine levels of 15ppm.

Keep your pump running 24/7 while you are trying to clear the pool.

Hope this helps. Come back with any further questions.