Dialing sounds like a rotary dial and the n it rings..

There is a feature called "Call Forwarding"
On most phones these instructions work.

Turning on Call Forwarding

1. Dial *72 (or 1172 on rotary phones).
2. Listen for three beeps followed by dial tone.
3. Dial the phone number to which your calls are to be forwarded.
4. If there's an answer at the number you are forwarding to: Make sure you keep the line open for at least 5 seconds to activate the service.

Turning off Call Forwarding
1. Dial *73 (or 1173 on rotary phones).

Sounds like bad wiring or connections.

Whats a rotary phone? J/k we're not that old yet.

Because phone systems are no longer analong. The way a rotary rings is by an increase in line voltage.

Check underneath. There may be a little lever there that controls whether the ringer works or not.

To change the dialing from pulse to dtmf dialing on a prostar 816 you first need to be at a display set (doesn't matter what the extension number is).
with the handset down, enter #20 the screen should say MMC DISABLED
1) enter in 1 2 3 4 1 # (that enables programming)
2) enter in #42 the screen should momentarily say trunk dial typethen display the current programmed data (00000000)
3) enter in 0 for pulse dialing and 1 for dtmf dialing for each of the lines. i.e. touch tone dialing for lines 1-4 would be 11110000. all 8 digits must be entered for the program to accept the data
press # when finished.

click on menu/setup button
then advanced fax setup-ok
answer ring pattern-ok
chose from single, double, double and triple, none-ok

I have a similar Panasonic phone (KX_TGA101S).  Someone must have inadvertently changed the dial mode on you.  Here is how you change it on mine, which should be similar to yours.  Hit the Menu button.  Scroll down to "Set tel line" and hit the Menu Button (OK). If it isn't displayed, scroll to "Set Dial Mode" and hit the Menu Button. Select Tone instead of Pulse and hit the Menu Button.  That should do it.

Since you neglected to specify the model of your VTech 5.8GHz phone I can only suggest you enter it into the search box here to download a copy of the manual to see how to switch from pulse to tone dialing.

Lisa, If the 900MHZ phone is Model 26928M programming for rotary dial usually goes like below, can't hurt to try on any model. TONE/PULSE DIALING This adjustment allows you to select tone (touch-tone) or pulse (rotary) mode dialing. The phone is pre-set for touch-tone use. To set to tone or pulse dialing: 1. Press and hold the program button for two seconds. You will hear a beep. 2. Press the *tone button to select Tone Dialing or press #pause to select Pulse Dialing. 3. Press the program button again. You will hear a confirmation tone.