I don't think that there is any real need for further testing of the woofer, as it should give sound hooking it up to the receiver. The further testing of it, if you wanted to do it anyway, would involve hooking up where the speaker wire normally attaches to the woofer. But no amount of testing is going to repair the woofer and magically make it work again. From what you have said so far, I think we can very safely say that the woofer is burnt out. It could be reconed, or it can be replaced, whichever is less expensive would be best. But before doing that, there is the question of whether or not the amplifier works. And given that the woofer is burnt out, that is a sign that either the amplifier is capable of putting out more power than the woofer can handle, or the amplifier is malfunctioning such that it damaged the woofer. Woofers don't burn themselves up.
As for the subwoofer amplifier, with it hooked up, you would measure it at its output (i.e., where it connects to the woofer). You would want to use "clips", not simply "probes", on the meter, as you will want to attach it and set the meter and then turn the amplifier on. You want to be careful about touching things when the power is on, or you may end up doing something worse than just damaging equipment; there is a reason why these things are referred to qualified technicians instead of having regular people play with them. In other words, carelessness or mistakes can result in injury or death, though most likely, these will not happen if you proceed with some degree of sense and caution. But, of course, I cannot promise you that you will exercise sufficient care, so beware and proceed at your own risk, or just stop now and forget about testing the amplifier yourself.
For testing for DC in the output, you would hook up the meter with it set for reading voltage. Start at the highest voltage setting, and once the amplifier is on, turn it to lower settings until you get a reading. Have no input hooked up to the amplifier. If the amplifier were perfect, you would have 0 volts, but we live in the real world, so it might have something like half a volt. If it is more than that, do not hook up one of your speakers to test it, as that is a sign that the amplifier is sending too much DC to the speaker. I don't know if the above is clear enough; I recommend searching online for more information on this topic, just to be very clear, or simply take the subwoofer to an authorized repair shop. Before doing that, you might want to ask what it will cost to replace both the woofer and the amplifier, as that will give you the maximum that it should cost for getting your subwoofer up and running again, if you choose to do that.
Assuming that there is no significant DC, you could try hooking up one of your speakers to the subwoofer amplifier, but if you made a mistake in your DC test, you could easily destroy the woofer in the speaker you hook up. If you choose to do this anyway, you should get sound when the subwoofer amplifier has an input. Obviously, you would try this with the subwoofer's volume control turned down low, as you don't want to destroy the speaker with excessive power. If you got undistorted bass that way, then it would show that the amplifier is working. It would then cause one to wonder what caused the woofer to burn out, though if you had the level turned way up on the subwoofer just before it failed, it is possible that the amplifier design is such that it can give excessive power to the woofer. Frankly, though, I would be surprised if your amplifier is working properly. My
guess is that the amp failed, causing the woofer to be damaged. I freely admit that that is a guess, but as I said before, woofers do not burn themselves out; something does it to them.
It is entirely possible that you will get no output at all from the amplifier, as it is possible that, when it failed, there was a surge of power destroying the woofer, and then complete failure of the amplifier. If that is the case, then hooking something up to it would be perfectly safe, and you would get no sound. But if the amplifier is outputting DC, it will destroy woofers.
I would talk with Velodyne about the cost of replacing both the woofer and the amplifier, to see if that would be a reasonable cost or not.
As far as making a new subwoofer is concerned, you will need to ask someone else about that. You might be able to use the subwoofer cabinet that you already have, but the woofer you select would need to have the appropriate parameters for that size box. Again, you will have to ask someone else about that.
For buying a new subwoofer already made, I don't have any advice in your price range; you would need to ask someone else. But if you could go just a bit higher, you could buy:
http://www.svsound.com/products-sub-box-10nsd.cfm
That, with shipping, will probably come in just under $500, depending on where you are. It gets glowing reviews, both professional and from individuals, for a subwoofer at its price point. Note its size before ordering, as some people are surprised by how big SVS subwoofers are.
