If like me, you like your music loud you really need a decent power amp. The Pioneer AS500 is on sale at a really good price these days and gives a lot of bang for the money (£200, 70W per channel). I have one and I love it but obviously it is not the most exotic amp around.
If you use an amplifier so that it is clipping and it seems likely that you have, you will only start to hear this when it is severe. Using a 30W amp to drive speakers that require more is more damaging than using a high power amp (sensibly) to drive low power speakers. Clipping starts when the amp is going flat out and there is simply no more voltage available. If the power supply to the output stage is +/- 30 V say, the output transistors can never reach this point and so the maximum useable swing will be about +/- 25V before non-linearity creeps in.
Into an 8 ohm load this gives an rms power of 39W maximum. As you turn up the volume control still further and if you look at the waveform with a scope you would see a solid line forming at the top and bottom as the amp spends more and more of its time at the extremes of its travel (voltage wise). The power output still rises because the form factor of a square wave is larger than a sinusoidal one. Taken to extremes this would become a square wave. Ragged waveforms of this kind contain high energy odd harmonics of the fundamental, extending way up the frequency range. It is these that cause damage, usually to the tweeter units. It starts long before you hear it but eventually it sounds awful!
As Vladimir has said, gently pushing the cones of the bass drivers without touching the dust covers will reveal any distortion of the speech coils which can rub on the magnet pole pieces when this has happened. You will hear a rubbing sound. When this happens the distortion you hear is worse at low levels than at high levels because it is in the mid range of travel (where the cone spends most of its time at low level) that the rubbing is usually (but not always) most noticeable.
Push evenly and gently, applying pressure evenly at several points around the cone. It is possible to bias the cone to one side so that the coil rubs because of this rather than an inherent fault.