The T6310 is a disposable radio. Assuming the programming is correct, and matching on each of your radios, and you are using good batteries, there is nothing which can be done to correct the problem. We would however, suggest you double check your programming, and also the age of your batteries.
Sidenote: Rechargeable batteries only last 18-24 months before they begin to fail. Signs of failure can include, but are not limited to, poor transmit, intermittent transmit, white noise, squelching sounds. It takes more energy to transmit than to receive, so your transmit would be the first to go.
Here is a link to the user manual: http://www.giantintl.com/ContentManage/manuals/Moto/T5320_T5410_T5420_User_Manual_E.pdf
This unit does not have a reset button. While troubleshooting you might check the batteries. Be certain they are in correctly and the contacts are free of corrosion. You can use a pencil eraser to clean the contacts.
Walk through all the programming instructions in the manual, double checking both the frequency and interference eliminator codes. A quick setting back to zero on the code would alleviate any problem with that section of the radio.
As far as your "paging" this operates on the same frequency and code as the rest of the radio. If the radios are not working correctly in this relm, the paging will not work either.
In addition to the channel and privacy codes, some Motorola two-way radios have a feature called Eavesdrop Reducer where you have 3 scramble settings available; perhaps you have this set on one of sets of radios but not the other. It should be something like that because otherwise there is no reason that by setting the radios to the same channel and privacy code they wouldn't be able to send/receive to each other.
Here is a link to the T5000-T5500 user manual. 'http://www.motorola.com/mdirect/manuals/T50-T55_UserGuide.pdf'
From what you have stated, I can discern the radios will power up. You might try setting your interference eliminators to zero (off) to see if you are able to transmit at all.
You do not mention if you are using AA batteries or rechargeables. Either way a fresh set of charged batteries would be best for a test. It is clear you were getting power. However, it does take more energy to transmit than to receive. If your batteries are low or bad, pressing the PTT could us all the energy the radio has, and yet not transmit to the other units.
You might also check you VOX settings if any and be certain they are turned off.
It is not likely 4 radios would fail all at the same time. So it is probably a programming problem. Hope the user manual helps you find the solution.
Use scanning to monitor channels for transmissions or to find someone
in your group who has accidentally changed channels.
1. Short press MENU until the "Z" appears. The current setting
On/Off will flash.
2. Press either + or – to turn On or Off.
3. Press the PTT to confirm or MENU to continue set up.
Here is a link to the manual http://www.motorola.com/mdirect/manuals/FV200_userguide.pdf
Your radio is in scan mode. You can shut off scan by referring to page 8 in the user guide http://www.giantintl.com/ContentManage/manuals/Moto/T4500_User_Manual_E.pdf