240 V outlet is not delivering 240 V
I bet if you go to your service panel, you're going to find a completely full service panel, and a unique creature we call a "double-stuff breaker".  Quite likely the landlord does his own electrical work or pays a dumb handyman (naughty naughty).  He's out of space in the panel, so he resorted to those double-stuffs. 

He moved the dryer from a 2-pole breaker (which takes 2 spaces) to a duplex breaker that takes only one space.  As my link discusses, one space sees only one pole, so you get what you saw.  Any proper electrician would notice a "red flag" where the duplex sides can turned off individually, making it unsafe for dryer use. 

Since this is a rental, you can't fix any of this.  Most jurisdictions require commercial work be done only by licensed electricians, and rental properties are considered commercial. You can't, he can't, his handyman can't.  A pro electrician is required.  

Given this level of incompetence, I would not advise trusting that circuit.  The obsolete and dangerous 3-prong connections absolutely rely on the neutral wire being intact and not broken.  If neutral breaks, the chassis of the dryer becomes electrified and can kill you, especially as you are handling wet things and touching both dryer (electrified) and washer (grounded). 

But since he must fix it, he should consider bringing in someone competent, and upgrading the circuit to modern, safe NEMA 14 standard.  This will require you change the dryer plug (back to what it was shipped with), but will be much safer for your family.