I would say it's more likely screen/backlight.
If it was just the inverter, the screen would still work but be very dim (almost black).
Shine a torch to see if you can see anything.
When I knocked my 2 yr old laptop (3 months at time) off an 18" side table onto carpet, it actually cracked the screen fairly obviously.
New screen cost me £70 from amazon
They are bit cheaper now, but you might have trouble with an 8 yr old laptop.
Replacement was easy for me (I am an electronic engineer). There are loads of Youtube vids and of course mfrs Service and Maintenance Manual Guide pdfs to help. If you are practical, it is certainly doable.
But if pennies allow, you might want to consider a new laptop and connect your old Hard Drive in a caddy via USB to transfer everything over.
Old applications won't transfer, but there are lots of Freeware sites for most things (unless you have something special)