Samsung m300 incomming calls go straight to message service

This is most probably call forwarding enabled for all Calls. Disable call forwarding and you should be fine. The other possibility is that you have barred incoming calls

Check video for 'fax receive set up' in similar model:


Manual receive: In coming call receives like telephone
Fax/tele: Incoming call rings like telephone if its not fax, if incoming is fax it will entered in fax mode automatically
Automatic: Incoming call converts in fax mode after ring count ends( ring to answer option also avail in fax set up mode rage 1-6 rings)
Fax: Incoming calls straight away converts in to fax mode.( this option only for dedicated fax lines)
Set up your best option as per your requirement.

Ring count You can change the number of times the phone rings before the unit answers calls. The default setting is "4 rings". "Toll saver": The unit answers on the 2nd ring when new messages have been recorded, and on the 4th ring when there are no new messages. If you call your phone from outside to listen to new messages, you will know that there are no new messages when the phone rings for the 3rd time. You can then hang up without being charged for the call.
1 {MENU} 2 {V}/{^}: "Answering device" i {OK} 3 {V}/{^}: "Settings" i {OK} 4 {V}/{^}: "Ring count" i {OK} 5 {V}/{^}: Select the desired setting. 6 {OK} i {OFF}
MANUAL http://service.us.panasonic.com/OPERMANPDF/KXTG1032.pdf
HOPE IT HELPS GILES102

Follow the below instructions and you can remove the vibrate state. I have included a link to download the phone's manual as a PDF file.

Sound Settings
Ringer Types
Ringer types help you identify incoming calls and messages.
You can assign ringer types to individual Contacts entries,
types of calls, and types of messages.
Downloaded Ringers can be downloaded right to your
phone.
Preprogrammed Ringers include a variety of standard
ringer types and familiar music.
Vibrating Ringer alerts you to calls or messages without
disturbing others.
Selecting Ringer Types for Voice Calls
Your phone provides a variety of ringer options that allow you
to customize your ring and volume settings. These options
allow you to identify incoming calls by the ring.
To select a ringer type for voice calls:
1. Select Menu > Settings > Sounds > Ringer Type >
Voice Calls.
2. Select With Caller ID or No Caller ID.


http://downloadcenter.samsung.com/content/UM/200708/20070824101259031_sprint_m300_ug.pdf

how do l make my samsung s8300t ring longer?l keep missing calls because it only rings for about 10 seconds.

Answering a call:

When a call is received the phone rings and displays the caller's
phone number, or name if stored in the Address Book.
1. At the incoming call screen:
• Touch and slide to the right to answer the call.
• Touch and slide to the left to reject the call and send it to
your voicemail.
• Touch and slide the Reject call with message tab upward and tap
a predefined text message to send to the caller.
- I'm driving
- In a cinema
- I'm in class now
- I'm in a meeting
- Sorry, I'll call later
- or -
- Tap Create new message to compose a new message.

You may also click on this link to download the user manual for complete instructions with photos:

http://www.samsung.com/us/support/downloads/SGH-I897ZKAATT

Note:
"Answering a Call" portions is on Page 46

Looks like the basic functions of the phone are correct. Remain the answering machine. Are you sure it can act as an answering machine?
If it can act as answering machine the reason it is not doing so may be the following.

1. Answering function is turned OFF
2. Answering function may be ON but the number of rings before it answers is set too high.

I suggest you try the following
Call you phone. Let it ring at least 10 times. If it can act as an answering machine it will pick up the phone and read the welcome message, because most answering machines (the recent ones at least) answer after 10 rings even if answering function is turned OFF.

The phones that can be answering machines usually do have a display that shows the number of incoming messages, or a LED that flashes to let you know that you have new recorded messages.

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

Manual:
http://www.cellphones.ca/upload/manuals/samsung-sph-m300-manual.pdf

From Page 39 of the manual:


Selecting Options (right softkey) during a call displays a list of
features you may use during the course of a call. To select an
option, press the corresponding keypad number or highlight
the option and press . The following options are available
through the Options menu:
 (1) Key Mute/Unmute allows you to mute the microphone
on your phone so the caller is unable to hear any sound.
 (2) Turn Speaker On enables the speakerphone feature.
 (3) Set Whisper increases the microphone to its maximum
level. During a call turn on Set Whisper when speaking
softly or when the caller cannot hear your voice clearly.
This mode is useful in meetings or public places.
 (4) Call History checks your call log for Outgoing, Incoming,
Missed, and Recent calls. You can also erase the logs from
this menu.
 (5) Contacts accesses the Contacts menu.
 (6) 3-Way Call allows you to talk to two different people at
the same time. (For more information, see “Making a
Three-Way Call” on page 189.)
 (7) Messaging accesses the Messaging menu options.
 (8) Voice Memo allows you to record incoming audio from
your conversation. (For more information, see “Managing
Voice Memos” on page 135.)
 (9) Tools accesses the Tools menu options.

Manual:

for the folks that are ending their calls by closing it, you can change your settings so that it won't do that. under settings choose how you want to end the call.