So, I still don't have a good idea of what exactly is giving you trouble (mostly because I didn't ask the right questions), but I think that we've narrowed it down to the point where I can post an answer of reasonable length.
When it comes to playing fast, there are a handful of types of figures that will give you some trouble. I'm going to cover repeated chords, tremolos, and arpeggiated/scalar figures. I think that you'll be able to effectively categorize whatever is giving you trouble with one of these.
To be clear, when I say repeated chords, I'm referring to something like this or this. While you can build up your hand speed, you're ultimately limited by how quickly the action of your weighted keyboard can bounce back. On an unweighted keyboard, the rebound is so rapid that you're incredibly unlikely to move faster than it. That being said, you're best off isolating the vertical, striking motion of your wrist from the lateral motion of the rest of your arm. Your wrists should never move up or down. It's very tiring at first because you are moving some of the effort from your upper arm to your forearm muscles, but you will be much more accurate and much more rapid once you develop the musculature. If a figure with repeated chords does not allow you to play quickly enough, you may attempt to substitute the chords with a tremolo.
When I mention tremolos, I'm referring to something like this, where the left hand is rapidly alternating between two notes (or chords). For this technique, you cannot move faster than twice as quickly as the piano's action. The technique I advocate for tremolos also isolates your wrist motion. Instead of a vertical up-down flexing, your wrist should rotate. To do this, you need to position your hand so that the axis of your wrist's rotation evenly splits the fingers performing the tremolo. This should not be particularly difficult to learn, and merely requires a little bit of practice.
Finally, for scalar and arpeggiated sequences, you are only limited by your hand speed. For these types of figures, you need to build solid fingering and practice a lot. Start slowly and make sure that you work out the most optimized fingering. Ideally, there would be very few jumps (to reduce error) and as few crossovers as possible, while still being comfortable to play. After you set your fingering, practice it slowly while paying careful attention that you do not waver from it. As you learn it, you can speed it up and you will soon be able to play that passage at speed.
I seem to say this in nearly every answer I post here, but it is extremely important that you avoid tensing up. Tension will ultimately lead to repetitive strain injuries (RSI, think carpal tunnel) over the long term (think decades instead of years). The worst part about them is that by the time RSI develops, you're fully committed to your instrument, and you'll have cemented those bad habits in place. So do it right the first time. Don't tense up.
That being said, whenever you try to push speed, you will fatigue your arm muscles, and they will tense up. You need to do your best to consciously relax your forearms when you play, and avoid "powering through" the tension. Take a break and allow your muscles to relax before continuing on.
Finally, Hanon's exercises are wonderful tools for building up the musculature necessary for playing rapidly. I believe there are exercises for each of these sorts of figures. However, I would only recommend practicing those exercises that mimic the figures giving you trouble. In my opinion, the exercises are quite boring and are a means to an end. It's a waste of time to practice hand motions that you don't need to and may never use.
If I have overlooked anything important, please comment on this answer so that I can tailor it to your situation.
