MB Pro (2009) is not getting power

Disconnect the battery. See if their is any signs of life when pressing the power button. This laptop should be able to power on & boot without the battery connected.

Look for an flash/flicker of light on the Display, look for the power on/sleep LED, see if the fan(s) spin at all (IIRC, they spin momentarily at initial power on, if not spin slowly all the time), any startup chime, hear the Hard Drive spin up or the optical drive?

Try an SMC Reset and PRAM Reset (the latter only if you see fan spin, LED light, display flicker, HD & optical drive noise and hold it for at least three chimes).

How long has it been since this laptop was last used?

Were there any issues of any type with the laptop before this "power on" issue occurred?

See this Apple article for some troubleshooting tips for Magsafe charging issues:

If your MagSafe cable or power adapter isn't working - Apple Support

FYI, you should be able to access the backups from another Mac. You just need to Option-click the TM icon on the menu bar so that "Browse Other Backup Disks...." appears as an option.

User_Gh482y-S wrote:

Sadly, I cannot access the external Seagate drive. It may have been corrupted. When I plug the drive into the other computer, it's unreadable. Is there a way to take the hard drive from the old laptop and access it thru 3rd party hardware?

You can remove the internal Hard Drive and connect it to another computer using a USB to SATA Adapter, drive dock, or external enclosure.

A USB to SATA Adapter may be the least expensive option:

https://tripplite.eaton.com/usb-3-0-superspeed-sata-iii-adapter-cable-uasp-2-5in-3-5in-sata-white~U33806NSATAW

Will the computer run on its charger?

Replacement batteries are notoriously awful. Apple have not sold original batteries for that model for years. Even if you found a original battery that is not counterfeit. ti would have been sitting in inventory for ages and will, by now, have died of old age.

So it may simply be a battery built on a Monday in a county not on any map.

Did you double-check that the battery cable is fully seated to tis connector on the logic board?

Be sure the MagSafe contacts on both the power cable and the computer are clean. Many power issues start there.

If you can start on the charger, do an SMC reset using the "Intel processor" section of this Apple article:

Reset the SMC of your Mac - Apple Support

User_Gh482y-S wrote:

Before the whole power failure, the laptop had always been in sleep mode and was rarely shut down prior to this. On its last wake-up it didn't respond properly, so I tried the PRAM reset. After shutting it down completely, it never came back up. My first instinct was that the battery was bad (after all, it's a 2009 laptop). So, I ordered a new one and it still had no power.

When it's plugged in (sans battery) the "idiot" light doesn't illuminate.

Edit: The MagSafe cable has a very feint glow, but the laptop does not power up.

Faint glow indicates a hardware issue of some sort.

Did you unplug the power adapter from electrical outlet to reset the power adapter which is one of the troubleshooting steps in the Apple article I linked in my last post? You can also try using another electrical outlet on a different electrical circuit.

Or an SMC Reset?

Anything else will require access to another power adapter or will require spending money if you don't have access to another compatible power adapter (preferably a known good one) or having the laptop repaired (doesn't make economical sense).