No dead hard-drive problem, it's just the thermal paste that ACER use that is crap!
I own an ASPIRE 1604LC, 9 months old and after a lot of SolidWorks, UT2004 and loads and loads of movie hours it started overheating until it simply switched off (precisely when I most needed it to finish my studies...)
I've checked that it was a cpu overheating problem with Hardware Monitor (which is Aspire compatible) running the Prime95 torture chamber until it crashed as usual (@84ºC)
I decided to open the computer since I could not afford being without it for one or two weeks for repair (it's still in the warranty period). After several atempts I've found out that it's pretty easy to open the Aspire 1600 and access the cpu:
1) open-wide the screen in order to completely expose the hinge cover (where it says Aspire 1600-it's actually just a lid);
2) remove each hinge cover by hand and with the help of a phillips screw driver (to pull them up);
3) unscrew the power button;
4) unscrew the keyboard (3 screws);
5) detach the keyboard pulling it towards the screen;
6) you now have access to the cpu cooling unit with 4 screws to ...err unscrew.
You should be able to see that the thermal paste is totally dry. I've just cleaned the old one and spreaded some brand new one and my laptop is down from 75-83ºC to 55-75ºC. It's still a rather noisy machine though, but that's a diferent problem...
Regarding the blinking battery light: it means that the battery is above 95% and below 100% of its capacity and won't be recharged to save its life... you need to use it a bit and then reconnect the AC power back on...
Hope this was useful!