The cup caused a damage in the touch pad, the touch pad is connected to the system board, first you need to watch a youtube of how to take off the keyboard, it should be simple, you will need to remove the battery, and any source of power. unscrew the back cover, you will see two screws underneath that has a keyboard symbol, remove them, they flip the laptop, open the lid, slide the keyboard toward the screen, and take it out slowly, flip the plastic piece holding the keyboard cable to the system board. now there is a small white flat cable that is connecting the touch pad to the system board, remove it from the system board side (again flip up the plastic piece attaching it to the keyboard, after you disconnect the cable, plug the power in, and turn the laptop on. IF it turns on, shut it down and buy a new touch pad from ebay, used ones will be better (cheaper) but make sure they accept returns just in case.
if you want, and you are capable of installing it yourself, assuming your existing one is broken, then get the Part # and look into ebay, if this laptop does not support wifi cards, you need to buy the usb wifi card, make sure it is compatible with your os.
what is the model of your lenovo. some lenovos power buttons are built into the system board. if this is the case then you will need to replace the whole board. try to find used boards on ebay to save money, but make sure they accept returns.
If you are saying it is cracked then it needs to be replaced. Check on ebay for the part cost. I usually unscrew the screen and check the model number/ part number on its back, and use this part number in ebay search. once you find the item, buy it and replace it yourself, Watch youtube to learn. If you do not feel comfortable doing it yourself, seek professioanal help. ebay link for a new one: http://www.ebay.com/itm/like/19073175933... a youtube of how to replace it: https://www.youtube.com/watch?v=WdZ-iZzW6V8
remove ram and then see if the screen turns on, if it does then it is the RAM, Do the same with hdd, if it turns on then its the hdd, also try to open the screen and check if the connector is loose other wise it might be a mother board issue,