It is possible to damage your computer by mining in the following ways:
- the computer will degrade more, as it is used more (you will have to replace it sooner than normally)
- the computer will overheat and some components will fail because of that (if for example, the computer is dusty. If the parts are well-maintained and the computer is not boxed in, this shouldn't be the issue)
- you will overload some part of your computer with the mining and it will short circuit or blow a fuse (mostly relevant if your power supply is weak, this happened to me once)
Number 3 you should notice quite fast if you run your miner at top speed, full load. If you are already mining, this probably won't happen unless you increase your load, or are operating close to the limit of your hardware. If something flashes, smokes, or the computer doesn't turn on any more, this was probably the cause. Replace hardware.
Number 2 you should notice if you run your miner for about an hour, once everything heats up well. Again, if you are already mining and this doesn't happen, it probably won't if you keep your computer clean and give it some air. If your computer turns off suddenly, but runs fine after cooling down, this probably was the cause. Clean your computer chassis, possibly add some fans or replace hardware.
Number 1 you won't notice for months or years.
Mining with lower-end GPU should be fine in all the regards, asides maybe 1 (leaving your computer on for longer to mine will ear it down more). Usually it means you won't use as much power and generate as much heat, so you should be fine.