Make sure your handset has atleast 10mb free. its all to common that most are not aware the handset needs free memory/cache to operate functions on the handset.
a good rule of thumb is for every 10mb leave 1mb free. also check the size of your photos and apps. in some cases some will say that they only have 2 pictures on there handset but in reality the size of those two pictures especialy if there high resolution will consume the majority of spare memory.
if you dont already have a memory card or the handset supports mem/flash cards then install one and move as much data as you can to the card.
Also check if your handset is 3g supported, if this is the case take into mind that some handsets seem to have an issue with 3g. if you use high speed internet or video calling then your option maybe to leave things as they are but for those who iether want to test the handset or just switch off 3g reception to avoid freezups and signal probs change the network mode.
usualy in the settings of the handset under the network or phone settings you will find and option called "GSM/3G", "Network Mode" or "Type". if you have this option change the mode to "GSM Only", "GSM 1800/1900 (UK & Europe)" or "1900" for any other. where you are in doubt call your network operator for a walk through or help or alternatively consult the manufacturer handbook or website for help. if calling your operator be sure to call from another device or line as you will need your handset free to complete the task.
Another common fault is to make sure the battery contacts are clean and undamaged, also you could try a second battery if you know of or can get use of a spare to test the handset with.
The last thing you can also try is to make sure the sim is securely inplace and free from any static, grease or grime. use a pencil eraser to remove any dirt and static from the gold contact/chip on the card. some people are told to wipe it on clothing but in alot of cases this will only ensure more static charge to the chip.