monitor with current leaκage issues
Of course there is a risk. It sounds like you have "lost" the internal earth connection entirely. This will likely mean that any internally bonded metal parts will acquire a voltage that is about 50% of the line voltage. 

The 50% figure comes from the live and neutral capacitors used to reduce conducted emissions. Those capacitors will also bond to local earth and with that local earth being disconnected from proper earth they will form a potential divider raising all internally earthed parts to 50% of your supply voltage.

That is why you felt a tingle in your fingers. There could be a serious safety issue here but without knowing the types of capacitors on live and neutral you have to assume safety is being compromised.

So, will it damage other apparatus connected to it. Yes it could but without knowing how well the "other apparatus" is at protecting itself it's impossible to say.