Hitachi SR-2000 receiver's right speaker connection does not work

Not familiar with the model. Remote speakers are just added speaker option if "main" speakers are not used.
Main (livingroom speakers) or Remote (bedroom) or both can be used via switch. Just observe impedance your unit may allow.

The answer is "Yes"

I had the same problem. You must turn on the remote speakers via the reciever and then adjust the remote speaker volume control that is only located on the remote control. The volume buttons are on the top right of the remote. It is briefly discussed in the owners manual which can be downloaded online.<!-- from fixya rte -->

Disconnect your speaker wires at the receiver,then test if it does not "peak" the receiver is fine and you need to check each speaker wire. re-connect one speaker at a time and test until it peaks. then disconnect at speaker and test again. if it peaks, it's a bad wire, if it does not, check the speaker, meter it for a short. If you still need help, post a comment and I can help you some more.

Remove the bridging links from the speaker terminals and run two equal lengths of speaker wire from the amp to the speaker. At the amp - speaker terminal, twist two of the same wires together. ( normally marked with a tracer color) Connect these into your left speaker output - terminal and tighten. Connect the two wires to both the negative terminals on the speaker. Repeat the same for the + side. Make sure wires are not shorting across the terminals.

I wrote most of this for a different receiver, but if you account for minor differences to your receiver this will work just fine.

There's good news and bad news. The bad news you need a separate amp because a multichannel receiver with Bose 901's attached as recommended for a standard stereo receiver will only sound right in STEREO on stereo analog material. The other speakers around the room are not designed to receive its Active Equalization and if you engage your Tape Monitor you will NOT BE ABLE TO HEAR DIGITAL sources at all. Tape Monitor is for analog stereo material only and on modern AV receivers it disables any digital inputs so you really can't use the Tape Monitor circuit or attached devices for modern digital sources. However, you can still employ the various DSP options to spread 2-channel analog source material around the room. I do.

The good news. I have a setup similar to what you want to do and it works great! I see on the SR875 there are Pre Audio OUTS. This is easy.

A separate stereo amp for the 901's was my solution. I run a Carver AV-406 (5-channel amp) for my 901's in Front, 2 Subwoofers and the Rear Surround channel, with the Active EQ between the receiver Front L&R Outputs and the 901's amp channels. My receiver controls everything and just drives the Center and Surround speakers.

You could get by with just a stereo amp for the 901's. A Carver M-200 is a good efficient amplifier that would have you cooking just fine (2x100W). Run it with the Active EQ between the receiver Front L&R Pre-Outputs ** and the 901's amp channels.

** Front Pre Out >>> Bose EQ Amplifer IN, then
Bose EQ Amplier OUT >>> new amplifier IN.

Attach the 901's to the new amp, set its volume to Max and run through your receiver's speaker level setup.

Hello, I am sorry about your issue. I suggest that you contact Onkyo product support at 800-229-1687 option #3 so that we can troubleshoot with you. Thank you, Onkyo USA.

No. Active Equalization is required for the 901's and not to be used with any non-901 speakers.

The Denon 2500 was one of the best ProLogic receivers built, it was a work horse and very little ever went wrong with them.
To make sure you're only supposed to hear right & left speakers, press the Stereo button on the remote. Also recheck your speaker connections - this is the single most overlooked connection problem folks have.
Check the balance control to make sure it's in the center position

Make sure the Tape Monitor is not engaged.

Then, check to make sure that the Pre-Out, Main-In jumpers are connected properly on the rear panel.
If that is not the problem, try pressing the Tone Direct button on the remote (aka Tone Defeat on the front panel).

theres probably a problem with the right channel cable or plug that connects the tv to the reciever, or the tv is set to mono audio.

Generally, crackling noises come from anyplace there is a mechancial connection for the sound signal. The volume control, main/remote speaker switch and possibly the headphone jack. That is where the contacts must be cleaned, but it requires dissassembly. Try operating the main/remote speaker switches, and plug/unplug a headphone several times. I am assuming there is still audio behind that crackling. Are you using both main and remote speakers simultaneously?