It seems you have a 2007 MacBook.
What was the upgraded memory you installed? Macs are very picky about the memory they use so it is best to only use memory from Crucial or OWC. Even then you need to use the tools on their respective websites to get the exact part numbers that are compatible with your Mac.
You don't need a battery to test the laptop as long as the charger is working to power the laptop which it sounds like it is doing.
My guess is you have a bad hard drive unless the Lion DVD is interfering with the boot process. Try a PRAM Reset (hold it for at least three chimes). It is possible you did not fully seat the memory as the memory is a bit difficult to fully seat as it can be very tight & awkward. Also this model had the original memory ship with a white powder on the memory contacts which I like to clean off using a pencil eraser and Isopropyl alcohol since I think this substance ends up interfering with the memory.
If you have trouble booting this laptop with the hard drive, external hard drive/USB stick, or OSX 10.6 Snow Leopard DVD, then I suggest you create a bootable Knoppix Linux USB stick to see if the laptop will boot when you disconnect the internal hard drive (and possibly disconnect the optical drive). You can use the downloaded Knoppix .iso file as a source for Etcher (Mac/Windows/Linux) which will "burn" a bootable Knoppix USB drive. Make sure to get the file with "EN" in the name for ENglish. I think the DVD image for v8.6.1 will work, but if not, then get the CD image for v7.x if it is still available. I haven't tried booting Knoppix on this model laptop in a long while. Option Boot the Knoppix USB drive and select the orange icon labeled "EFI". While Knoppix is booting the Mac may appear frozen on the Apple boot picker menu so give Knoppix lots of time to finish booting.
You can also use Knoppix to check the health of the hard drive by clicking on the "Start" menu icon on the lower left corner of the Taskbar and navigating the menus to "System Tools ---> GSmartControl". Within the GSmartControl app double-click the drive icon for the laptop to access the drive's health report. Post the complete report here so I can verify the drive's health.
To eject a DVD you can hold down the Trackpad button as you power on the laptop or you can Option Boot the laptop and press the eject button. Many times the optical drive slot opening in the case can become pressed together making it impossible for the DVD to push through. Other times the felt within the optical drive slot opening becomes stiff from liquid damage or the felt may actually come loose from the frame blocking the opening and preventing the DVD from being able to eject. If this doesn't let you eject the DVD, then you will need to remove the optical drive and remove the cover to access the DVD.
FYI, OSX 10.7 Lion does not come on DVD. While it may be possible to somehow create a Lion DVD installer we will have no idea if it has been done correctly or whether the burned DVD is any good. Besides you are better off with OSX 10.6 Snow Leopard unless you need to update the system firmware to allow the laptop to use more than 4GB of memory. At least with OSX 10.6 Snow Leopard you can use TenFourFox and Rosetta to get a backported version of Firefox that can work on this laptop. Unfortunately I just saw that the developer of TenFourFox is stopping development after the next release so I don't know how you will get this laptop to browse the Internet later. OSX 10.7 Lion has a severe unpatched vulnerability that can be exploited when connected to the Internet.
If the laptop has a minimum of 2 or 3GB of memory, then installing Linux on the laptop would be a better option since it would give you access to the recent versions of the popular web browsers such as Firefox, Google Chrome, and Vivaldi. Linux Mint or one of the Ubuntu flavors such as Kubuntu or Ubuntu-MATE are good choices for a memory restricted computer plus they look nice and should install easily on a Mac, however, I find 4GB is the best although I have used Linux with just 2GB on a MacBook.
