Yes Home Depot does install dishwashers and will deliver the dishwasher to your home and install the new one.
When you buy a dishwasher from Home Depot you can have them deliver the dishwasher and install it as well.
Home Depot will charge an extra $99.00 along with a $19.99 installation kit fee and a $9.99 adapter fee.
When you pay for those fees then Home Depot will arrange to have your dishwasher delivered and installed in your home.
The delivery and installation may take 1 to 2 days after you purchase the dishwasher and pay the installation fee.
If you can install the dishwasher yourself you can save some money and take the dishwasher home the same day.
Or you can still take the dishwasher home with you the same day and then someone will come by in 1 or 2 days when available and install the dishwasher for you.