I want to turn off the voicemail option for incoming calls and have the option to answer a call or to let an incoming call go unanswered without the option to allow incoming callers to record a message.

From the sound of it it I think its either: your mailbox is full or the feature has been turn off accidentally.

Vtech's support recommend the following (I've removed things like 'make sure its plugged in' and 'is your answering system is turned on' etc..)

1 Some answering systems have an announce only option, which plays your greeting but won't record messages. Make sure your system is set to record messages.

2 Your answering system's message capacity may be full. You must erase old messages to make room for new ones.

3 If you have voicemail service in addition to your answering system, your caller's message may be going into voicemail before your answering system picks up the call. Program your voicemail to pick up at least 2 rings after your answering system is set to answer the call.

Your phone is set to "answering machine" mode. Find the option and turn it off. Call your service provider if necessary.

Call services From your phone, you'll be able to access and change the settings of various call services for your phone.Contact your mobile operator to find out about the availability of call services. From the Home screen, press MENU and then tap Settings > Call. Fixed Dialing Numbers Restrict outgoing calls to a fixed set of numbers. To enable this feature, you must know your SIM card's PIN2 code.
Voicemail service Shows the current voicemail service being used.
Voicemail settings Specify another voicemail number aside from the voice mail number on your SIM card.
Clear voicemail notification If you have a notification of a new voicemail, you can clear the notification with this option.
TTY mode Enable this mode to connect and use a compatible TTY device with the phone.
Hearing aids Enable HAC (Hearing Aid Compatible) to amplify in-call volume.
Phone settings Edit the call reject message, choose whether to open the message editor when you reject a call with a message, and choose whether to allow automatic saving of an unknown contact number when a call with that number ends.
Cell broadcast Enable or disable receipt of cell broadcast messages from your service provider.
Cell broadcast settings Configure channels and language for cell broadcast messages.
Call forwarding Select how you want your phone to handle busy, unanswered, and unreachable calls. You can also set the call forwarding option for all incoming calls. Call barring settings Choose whether to block various categories of incoming and outgoing call.
Additional settings Enable or disable operator services such as caller ID and call waiting.

Without a specific make and model from you, I dont know about your phone specifically, but most cellphones,if you press the End Call button while the phone is ringing, it will reject the call.

Most cellphones send the caller to voicemail when the call is rejected. Some simply cut the caller off.

I am almost certain that this will work, I have yet to see a cellphone that doesn't.

Make sure you have Any Key Answer turned OFF in your Call Menu...

Some phones let you choose which activity answers incoming calls. Most options are Answer Key to answer, Any Key To answer, or Flip Open to answer. Choose the Answer key Only to pick up calls.

Then, when you press the End Call button, your caller will be rejected....
Good Luck!!

Per the Sprint support site at http://search.sprint.com/inquiraapp/ui.jsp?ui_mode=answer&prior_transaction_id=2&iq_action=5&answer_id=33554455&highlight_info=6293864,0,6&turl=http%3A%2F%2Fsupport.sprint.com%2Fsupport%2Farticle%2FSet_the_number_of_rings_for_voicemail%2Fcase-ev207663-20090626-084943#__highlight&id16=voice+mail :
"A call will roll to your voicemail if unanswered after 23 seconds.
This setting can't be changed. However, on your Sprint phone, you can change your ring tone to one that reduces or increases the number of rings you hear before an incoming call rolls to voicemail.
For details about setting up and changing your ring tones, refer to the user guide for your phone."
If this is not the problem with your phone I suggest you call their support line:

Call *2 from your cellular phone or 888-211-4727 (Sprint phones) or 800-639-6111 (Nextel phones)
They may ask you to perform troubleshooting tasks, so it would be best to call from a phone other than the one you need help with.

Sounds like you need to set the call forward no answer to the VM pilot DN for the set with the new mailbox.

Go to call settings and cancel all the call settings information..
note: you will see call barring , call forwarding, call waiting options
just cancel all of them if it will not work, in the phone settings look for the answer call and change the settings there

Ok, do you know how to get into system programming?

If you do:
-> first dial FEATURE 985 this will give you the DN(Extn) for the voicemail
-> get into programming
-> TERMINALS&SETS enter and put in the extn that is giving you issues
-> then under CAPABILITIES look for FWD NO ANSWER and put in the DN of the voicemail you saw with the Feature 985
-> hit next for the number of rings you want it to ring before going to voicemail
-> hit next and you can now RLS to back out of programming.

Voila, that set will now goto voicemail.

You want to make sure your callforwarding is on. Sometimes when you select sleep mode, the calls will divert directly to Voicemail. Plus, ensure you have signal. Without signal, by default the calls go directily to voicemail. We won't wanna miss a call here. You can follow these steps here. start
settings
phone
services
call forwarding
get settings (wait for a while)
forward all incoming phone calls (check the box)
OK
OK
Exit

In the option to forward calls, there should be an option for the amount of seconds the phone RINGS prior to forwarding directly to voicemail.
IF your HTC device doesn't have the option for voicemail, and your calls are routed else where, contact your carrier for the voicemail number. This is very important!

Cheers!

if you have voice mail, you can set the number of rings before forwarding to voice mail in the administrative options of the voice mail menu itself. Call your voicemail and listen for administrative options. Follow the prompts.