Macbook mid-2010: no power after ssd upgrade
No light on a MagSafe adapter means it's not seeing the (one wire) charging circuit of your MacBook Pro.

So, this is unfortunately not a battery issue.  It's further confirmed by no fan spin and the fact that you eliminated the charger from the equation by testing it (successfully) on a different computer.

You may have shorted something during your swap or it could be just coincidence.  However, there are a couple of things to check before resigning it's a logic board issue:


check/clean your MagSafe port.  It could be just coincidence that your MagSafe port is dirty/blocked and preventing you from powering/charging your MacBook
double check your connections; you may have missed one or more or may have accidentally disconnected something.
check your DC In board. It's a relatively inexpensive part that's fairly easy to swap out.  If anything was going to "go" this would be the most likely part