One methodology (for non APN SIM cards) would be:

1) Drive Out 

2) put SIM card in phone 

3) browse internet from that phone using that SIM card 

4) if it doesn't work, phone your cell phone network and get them to sort it out

Reason: the network probably cancelled your SIM cards because you didn't make any voice calls

Where the modem simply does not connect to us, you must take it up with your network

of coarse before driving out to site, you can do some additional tests like
switching on delivery reports on your phone and then sending the modem an SMS to see if the SMS gets delivered
or phone the modem with a CSD call and check if it rings
if the SMS gets delivered or the CSD call rings, then the SIM has not been cancelled