Salt system shows low salt but we had it tested and it is okay, the pool store tells us we need a complete new salt system.

Salt system control units will give a reasonably accurate reading for the salt content in the pool, with one exception, when the cell has expired. You did the right thing in having the salt tested independently. Your service tech can test your salt for you and should be doing so as a matter of course every 3-4 months just to make sure the system is reading correctly and there are no other issues.

Many homeowners, when purchasing salt systems for the first time, are not informed of all the relevant information on the life of the systems. Do not presume that once you buy the system and have it installed it will operate tirelessly for the life of the pool. If we use the Hayward Aqua-Rite or Pro-Logic systems as an example, the cells used on these systems have an operating life of 10,000 hours. After that the life of the cell expires and the cell requires to be replaced in order to continue to produce chlorine. If the clients pool runs for 9 hours per day 7 days per week the cell will be required to be replaced in 3 years and 3 months.

A replacement cell for the Hayward system can cost up to $650 for another cell that will only last another 10,000 hours. Several manufacturers have developed aftermarket replacement cells that directly retrofits into the Hayward unions. They are cheaper than the Hayward AND they have a stated life of 15,000 hours, coupled with the fact that the cell itself is see through and the warranty is 3 times better than that of the Hayward, it appears to be a "no brainer", however, buyer beware, several companies that produce these aftermarket cells including Compupool have gone out of business, therefore so has any warranty

Personally, I would replace the system with the latest technology from JANDY. 
Jandy use proven technology to ensure that their units do not suffer from board failure with the slightest surge, a common complaint with the Hayward systems.