Will my current home theater speakers work on this new amp?

No, your old JVC systems speakers will not work with ANY other system. Such cheap crappy system speakers not only are LOUSY speakers, have odd impedences, and almost always use proprietary connectors such that you physically CANNOT use them with gear that uses standard audio connectors.

As Mac said, even if you were able to rig up a connection for your speakers, they would likely damage the new receiver that you are buying, by being electrically incompatible with it.

Proper home audio speakers have standard connectors, which consist of a pair of speaker wire terminals. Their being coloured red and white is to help you to keep the connections in phase, positive to positive and negative to negative. Similar to how you connect two car betteries together when jumping one of the cars.

On the issue of costs, I have to tell you that, adjusted for inflation, good proper audio gera has never ever been cheaper than it is now. My first proper audio receiver, a Harman Kardon 730, cost me $450 in 1976. In 2015 dollars, that would be closer to $2,000 than it is to $1,500. So, $300 for your proposed Denon is very, very affordable, as would be a proper set of 5.1 speakers.

Plus, a proper set of speakers will sound MUCH better than the crap you're presently using. Sorry to be so blunt, but that's the reality about such CHEAP speakers as such all-in-one systems have.

A third or more of all the questions that come up in the audio section here have to do with people suddenly discovering how limited a purpose HTiB equipment serves. Almost no one with the expectation of upgrading or expanding a sound system does not smack painfully against the boundaries of this sort of ill thought-forward appliance. Receiver and component audio is not supplanted by such appliances. It is not a forward move in technology. These are dead ended audio solutions. The convenience they offer is limited entirely to the saving of the extra half hour in a shop in picking out speaker sets. At a terrible future cost in usefulness. You live with them or toss them, sorry to say..

No. We never recommend the box home theater systems because they do not have parts that are swapalbe. When one part breaks - you toss the whole thing away.

In truth - you will probably damage a decent receiver if you try to put those speakers onto a 'normal' amp.

No it would not work and if it could it would sound terrible and blow up something. I took one for the team and done this myself with a Samsung hitb speakers and a Yammy avr and it was awful. Any stand alone and sold as surround speaker sets would work with normal regular avr's. Your proprietary jvc speakers, not a good idea.

Sorry, one of the joys of HTiB's is that no one piece can be upgraded. That is only one of the reasons AV pros sneer at them.