With mobile broadband there is also the possibilty that network aquisition is simply slow the time to start up and fully negotiate a 3G cellular data connection can range from as little as a few seconds to several minutes depending on a range of factors. Signal strength and quality is often a big one as is interference, you can often get an idea of signal strength from the device itself or a mobile phone using the same network though that says less for quality.
Have you a mobile phone on the same network if so try taking the phone removing it's battery and cold starting it to get it to completely lock onto the network from scratch as soon as it loads hit the web browser and see how long it is before you manage to load a major website. Count the time from pressing the power button to the page load as in general terms mobile phones have hardware to handle the network side that will be setting up while the software is still booting too.
If you have a poort signal this could be a fact of life the connections for mobile broadband can take longer than phones also sometimes as the latter are often deliberately run at lower data rates etc than the full mobile broadband data service by for example not using all the channels leaving less to test for usability in the connection negotiation.
If however all looks good for siganal and using a mobile phone to do it then the problem is likely the USB modem or perhaps the USIM contact your ISP they should be able in most cases to provide a new sim for free and if it is under 12 months old the modem too most likely. Trying another USB port might help preferably on a different hub (generally the front ports on a computer are a different root USB hub in hardware to the rear so swap them over. That will only apply however if the problem appears to be slow detection of the hardware not a connection matter.