You've gotten some good advice already, so there are only a few things I want to add.

1. Once you are able to maintain a strong chlorine level ALL the time, THEN you'll be able to start cleaning up the pool. How long it will take is more than we can answer. Using the clarifier you have MAY help, and won't hurt . . . . but ONLY if you do not use more than recommended. Overdoses of some clarifiers can 'work in reverse', making it nearly impossible to filter the gunk.

2. The Intex cartridges are low quality. Getting Unicel cartridges will help . . . if you clean them consistently and correctly. Here's how:
http://www.poolforum.com/pf2/showthread.php?18044 . There are also links to Unicel replacement cartridges on that page.

3. Test kits matter. A lot.
+ Here are links to the kits we recommend:
HTH 6-Way Test Kit @ Walmart
Taylor K2006A (3/4 oz bottles) @ Amazon
Taylor K2006C (2 oz bottles) @ Amazon