Although you might get something cheap and save it from going into landfill, still, you get what you pay for and remember, the practical life of a computer is about 5 years. The physical life of some computer components is shorter, especially if they are poorly made to begin with, or have been well-used. If you are getting a computer for something that is mission-critical, buy new, good-quality gear. It will last longer and be more reliable (and cost you less in the long run, instead of having to buy a number of cheap computers.
This is a great section on rechargeable batteries.