It is not going to damage your amplifier or receiver unless you crank it up to excessive sound levels that are inherently stupid...unless...that bad tweeter shorts out completely and your amplifier croaks as a result.

Since you already know the tweeter in that one speaker is defective, it is risky to use IT at all!!! It could be trouble.

MIsmatched speakers are not likely to sound all that great, however.

A SMART question would be something like this:

"My budget is $____ and I listen to ___________ and I am driving my speakers with a ____________ amplfier.

  What speakers would be the best for my budget?"

You may find that the BIC speaker does not sound as good as the old ones; that is my guess.

At minimum get another BIC tower. Better still would be to buy a pair of speakers that you'll be happy with.

What will you be driving them with?

What kind of music do you listen to?

How loud do you listen?

What kind of furnishings are in your room (describe room)?

Lastly, what's your budget?

I don't know what your budget is like, but I am going to assume that you want some fairly good large speakers for well under $1000.

Unfortunately the list of really good large speakers for under $1000 is a short list.

A friend of mine recently bought a pair of Mordaunt-Short Aviano 6 speakers, and is very happy with them. he especially mentioned their strong bass performance.

I see them on Amazon for $449 per pair, which looks like quite a good deal. I would look hard at them if I were you.

Spending a little now almost always means spending more later , and a little more later and so on . 

Buy once , buy right , save money in the long run and enjoy the music .