First of obviously you will have to sort the problem out with your password before you can move forward/Unless it is connected to the verification process, which then is outlined below; I'm proceeding with your problem best i can with the details you have provided, as i'am unaware of your overall competence in such matters, so please forgive me if I'm advising you on the obvious.
It appears that you are not a big mobile phone user, however, one is needed to verify it's you just for security, no expensive device on contract is needed, if you use Amazon a decent cheap 3G phone can be purchased from their site from as little as £15. Once purchased obtain a free Vodafone sim card from Amazon also, these cards can be topped up for as little as £5 without contract, choose the 'pay as you go service' and you can add money as when needed. The set up process is pretty much straight forward to get your sim up and running, the easiest way is to set up a debit card with them, this process is fully automated and once credit is assigned to your sim card, you can use that number to verify it's you when Paypal ever needs to send you a 5 digit number by text, which then to confirm it's you by sending the same number back, so you can move forward with what you are dealing with. There are also other means by which you can top up your sim card, and this changes by each provider.
To add, sim cards from different networks may be available at your local newsagent which you will get faster than waiting to be sent to you, Vodafone starts at £5 to top up whereas the other networks start at £10 (but please check) if you do have your newly purchased phone available, then the newsagent may be helpful enough to help you put the sim in, and help you set it up! If not then just follow the instructions being given from the phone!
I wish you the best of luck.
