broadband via USB dropping

My PC has no ethernet port so i use a USB connection for
my broadband internet connection. However the connection
isn't stable, after a variable amount of time (from
straight after startup to after 1-2 hours browsing) the
connection is dropped. The light on the ethernet to USB
converter shows continued activity however internet access
is lost. I have to restart my PC to regain connection each
time this occurs, however on shutdown after losing the
connection the PC hangs, giving me vertical
yellow/brown/black stripes on my screen, shutdown can then
be achieved by pressing 'enter' once. If 'Restart' is used
the PC also refuses to shutdown completely giving me a
black screen with a flashing cursor in the top left
corner, tapping 'enter' gives a black screen with broken
white vertical lines, then shutdown after further tapping
of 'enter'.
I have good free memory resources (over 90%) and this
still occurs.
Any ideas why this is occuring or what I can do to fix
this problem?
Thanks in advance