When I turn my N900 on with no charger plugged in, it displays a blue NOKIA logo on a white screen and wont go any further (no buttons work, only thing that works is yanking the battery). If I plug in the charger, it displays a dim screen with a NOKIA logo and then flashes the charging LED orange.

Does this mean my battery is just flat or could something more serious be preventing my phone from booting? (stuffed up config file?)

Battery being flat out is one reason so you may want to charge it first.

Another reason could have something to do with stuff that you did to your N900. Did you happen to have NITDroid installed?

I encountered a similar problem and I likewise thought it was the battery so I went with that as the first step (process of elimination). If the problem was solved then it's the battery (which was not, in my case). I tried to recall stuff that I did, between the last time my N900 was working, versus the first time I encountered the problem. Then I remembered having uninstalled/re-installed NITDroid. Also I remembered having missed a step in the installation.

So let's go with the first troubleshooting step (charge the battery) and we'll see from there. By the way, I have read that the battery won't continue to charge if you have totally discharged it so you may either need to charge it from another device, or an external charger.

get the battery out,let it cool for some time ,put it back,plug the charger ,turn on the phone and it should be fine ..

I have tried leaving it to charge for over an hour with no luck (wont get past the NOKIA logo)
I have not installed any 3rd party operating systems on the phone at all.
I can get the flasher to see it and if I do flasher -R to reboot it, it displays the NOKIA logo with a USB logo then it disappears back to a dark screen and the charging LED. If I run lsusb, it just says "N900 (Storage Mode)"

Is there some way I can tell whether my battery is flat (and just needs to be left overnight to charge or something), whether my battery is dead (and isn't properly charging) or whether my phone needs re-flashing somehow?

The best way to find out is do those things. Leave the battery overnight and charge it. If that doesn't work, you know the battery is either dead or it's not the battery. So then reflash. If that too doesn't work then the battery is quiet possibly dead, and you need to get a new one.

Did you ever overclock? Undervolt? Modify system files/bootup-scripts, etc?

flash it just by combine

no no ,it happened to me two days ago,phone was suddenly off and it was nt turning on ,i simply did what i told ya above ,it was battery problem,i even took my sim out and then simply put that back ,every thing was okey and yeah your battery must have some voltage to run beyond the nokia logo.hope your N900 get well soon.