Well from a cursory glance it appears genuine...but that is just that a glance..the plate with your info looks genuine. Hm
Now I do admit that perhaps taking the board out and giving her a once over may seem extreme ...but if you know how to do it ...it isn't a big deal...it may net more info...there are how to's on youtube etc..that show if you are leery of doing it without a visual guide.
But perhaps 1st.... an Ock. check. (Ockham's razor checklist ...that is )

Let's run on the best assumption 1st... the battery.

1- Get your hands on a tester ...see if it holds the charge or any charge at all. If it doesn't ...hopefully problem solved. Get a genuine n900 battery (best solution) or an alternative compatible brand that has had extensive testing here in the forums.
You would end up buying another even if the battery was fine. A backup battery or 10 never hurt

2- It is/ isn't just the battery... it is the cable you are using...
It may be possible to rule that out since you tried the proper cable.
(I do suggest using the approved parts and acces. and alternates that have been extensively tested here....using random untested cables or methods can have unpleasant effects.) Using those other cables may have toasted the battery...so that is the unknown at that point.

3- Not fun...it is the usb port. Hence some of the charge oddness (though I really hope it is just the battery)
It can be re-soldered ...that is the good news. there are how to's

4- It is the battery and /or the cable and / or the usb or it is none of the above....

5- Which could W.C.S. (worst case scenario) lead you into the possibility of fun with something really not good going on internally.

There are the potentials ...the known isn't so daunting as the unknown...unless I forgot something that is

This is in my very humble estimation what you are looking at all tolled.
Not a lost cause ...just a puzzle to figure out.