The battery is most likely not dead. 9 out of 10 phones returned for "dead battery" have batteries that test good under battery stress tests.
The problem is most likely one of two possibilities. 1) It's a failed boot process due to having been allowed to discharge until the phone was forced to power itself down. This can likely be resolved through one of several recovery or factory reset methods. 2) The battery was deep-discharged when you let it run dead, resulting in the voltage being so low that even on the charger it's insufficient to fire up the charging circuit and trigger the boot process. This happens when the demand for current from the deep-discharged battery is more than the charger can supply while also having enough left over to initiate the charging circuit. Sometimes this resolves itself if left on the charger for a day our two. Other times it calls for a more drastic measure.
The solution is often to simply bypass the phone and essentially hotwire the battery directly. This can be a very effective way to resolve a deep-discharged battery, but must be monitored closely and should not be left unattended. Direct charging a Lithium Ion Polymer (LIPO), battery, if left connected too long can result in over-charging and the consequences can be a battery that overheats and bursts into flame.
Direct charging should only be used as a temporary means to get the battery back above the threshold voltage where it once again responds to the charger using the normal charging method. When direct charging a LIPO, never charge for more than 30 minutes at a time and after each attempt, revert to the normal charging method first. If the phone responds and normal charging begins allow it to charge fully the normal way.
If after 3 direct charging attempts, the battery still will not respond to the charger the normal way, consider the battery a lost cause. If the battery begins heating up during direct charging to where it is too hot to hold, disconnect from the charger immediately, remove from indoors quickly and place outside on concrete away from flammables until cool. In either case, and once cool dispose of it safely (at a battery drop-off location such as the nearby Staples or your community's hazardous waste facility), and replace with a new battery.
Whatever you do, DO NOT keep old, failed Lithium Ion Polymer batteries "laying around". They may still have substantial power stored in them and over time they can begin to create internal shorts or "shunts" which can also cause them to overheat and self-destruct releasing dangerous high-temperature flames and super-heated gasses.
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