My internet is as crappy as usual, but it still works. Am sending and receiving emails, downloading videos, etc.
Possibly there is some security setting or anti-virus app on your PC.
Or maybe Google decided your speed was too lousy to give you all the bells and whistles.
Try an Internet speed test.
See
viewtopic.php?f=11&t=6830and compare your results, though mostly we get "Slower than 95% of Hong Kong", that should be enough to read email.
If you have a smartphone, try their GMail app and see if it can read it.