Is it still possible to mine for bitcoins using a normal desktop computer nowadays?
Yes it is Possible But Now a Days It's not Profitable Because Now a Days Even Mining is not Profitable Because you will get just 12.5 BTC for Solving a Block now and it will not Cover your Expenses So I Suggest you to Never do Mining with a Desktop, Do it with a Hardware.......
Even if it were a little bit profitable it would never last for long. There is always some huge mining farm that will just totally destroy you and your mining will be worthless. That's the problem with mining even with asics.thise farms just take over.