use a multimeter to test if the Alternator is charging. No charge. new alternator. Could be a tired battery as a tired battery can do funny things (reset radio) as cranking can take too much friom the system etc etc.
If you bought from a garage you should (legally) have a 3 month warranty. Whats actually wrong with it? It wont want it all changing. Are they tring to make some money out of you? Get a second opinion.