I have encountered many problems with the store before, however, a relogging has solved all of them.
If relogging doesn't work try this:
If you want to purchase a champion, when you hover over the box with the picture and costs of the champion, a circular 'i' button should appear. Do not click the top half of the box (the half with the 'i' button). but instead click the bottom half of the box. A pop-up should appear, asking you whether you would like to purchase the champion with RP or IP.
For runes, you can click anywhere in the rectangular box, there is no 'i' button. Then the pop-up should appear.
If this doesn't work, then can you please post a more detailed explanation, I am having a little trouble understanding what the problem is.