I wonder if valverde ever managed to access their gas bills online, I've been struggling with the same thing. The main problem is that Repsol's site is the most user-unfriendly and difficult to navigate of any company.
To start with, if you want to be able to place orders and view bills, it's not enough to register on the main Repsol site, you must also register as a 'client' so you can access the online services. Repsol had to tell me this, it doesn't seem to be indicated anywhere.
Then if you have a query or problem of some kind and send an enquiry or complaint via the website, you'll get an email of acknowledgement from Repsol with a link to your 'communications'. Clicking on this link takes you to a page with the details, date, subject, etc and the status (estado) of your question. However Repsol will not send you a further email to let you know they've responded. You have to keep checking back using the link until you see the word Terminada in the status box which means they've replied. The catch is the reply isn't visible, it will only appear if you press Visualizar in the box on the far right.
Finally, they've sent me a message admitting that at the moment Repsol's website only works properly using Explorer version 8/11. Apparently, the problem will be resolved "in the next few days". To add insult to injury, this message was sent all in caps.