RPM needle jumps, and car vibrates

[cashville]

Hi. I've been having a problem with my H2, when my car is in D or R, the RPM needle jumps a little bit, and the car also vibrates a little and I noticed a loss of power in the exhaust. By turning the lights on, I also noticed they sometimes flicker, like losing power.

I've also noted on the highway, that sometimes it looks like the car looses some power just for a millisecond, and keeps happening. I though it might be the battery, because it happened to me on the highway yesterday for example, so as soon as I got home I put the battery charging.
Today with the battery fully charged, I used the car for like 5 miles, and when I was waiting for someone with the car in park I noticed the exhaust sound kept changing its noise, like it was loosing power for a millisecond also. I then put it on park and noticed the rpm needle was jumping, so I made a little video:

http://www.youtube.com/watch?v=QxuSsdd6Qgk

I'm shiffting from D, N, R to P in the video, you can hear me do it, and the needle only jumps on D and R.


Because I'm thinking this might be a battery problem, I'm going to post pics of my stereo system, so you can have an idea:












This is all being run only on this battery:




I bought the car like this almost 3 years ago, I think this battery might not be sufficient for everything the car has, and maybe it's dying and the symptoms I'm getting are from it. I don't know for sure that's why I'm asking, because noticing loss of power in the car, and I mean wheel power on a highway (and it's really just for a millisecond, like little stumbles every 3 or 4 seconds) might be a symptom that excludes it being a battery problem, I don't know...
Any help would be appreciated.


Regards