Yeah it could be as simple as a valve inside that needs to be opened...I guess he could have closed that off in order for it not to freeze in the hose over the winter. At this point I'd just keep documentation of the attempts to contact your landlord without return communication, in case you ever need to show it to him. And go ahead and call a plumber to come out and take a look. But I'd call and email the landlord once more, explain that you need the hose for the party, etc., and that you know he's busy so you're just going to call a plumber to come out and will include the receipt of the invoice with your July rent...and take that amount out of your rent. Or if he'd prefer you handle it differently, then just to call or email you and let you know, because the plumber is scheduled to come x day (give the landlord about 3 days notice).
In chicago for most repairs tenants can send the landlord a 14-day notice to get it fixed and then if the landlord doesn't take care of it, the tenant can have it fixed themselves and then deduct from rent. But I don't think use of the hose would fall under the list of things that landlords HAVE to take care of. That's why I'd try the above approach and see how he handles it.