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I have about 20 old cell phones. I checked e-bay and there is no value in them as working units (too old). Am I better off leaving them whole or taking them apart?

You may want to pull out the cuircut boards and try selling them on Ebay. There is a little gold plated on the circuit boards and the dial pad circuits, but not enough to get crazy over. You may get around $10 on Ebay. Maybe. And thats only if you have the right type of old phones. If it were me, I would give it a try for the heck of it. I know the yard near me would just give me mixed metal shred for the lot, but some places may not want them because of the batteries. I would check if there is a market for the specific batteries on Ebay.

Find a place that either recycles them specifically, or can refurbish them for use for the Troops/homeless shelter/battered women shelter.

Cell phones are valuable as scrap, the main problems are accumulating enough of them and finding a buyer.

The circuit boards inside are very high grade but it's too labor intensive to take them apart. Most companies that recycle them send them through a shredder once the batteries have been removed.