I tried this method and unless I did something wrong, it did not work for me. After editing the DNS settings, there is no "OK" button to tap to save. Only the cancel button is highlighted.
I know this thread is a little old, but for K.G.B, this is how you can keep 3.70 while doing what they were talking about.
1. Boot up ps vita in safe mode (hold power+right shoulder+PS button)
2. Select restore
3. When it boots up. it will say the memory card is linked to whatever you PSN account is and will ask if it's yours. Say no and that you do not have an account.
4. Format memory card
5. when everything boots up, go to settings/system and make sure to turn off auto update
6. now go to network and set up your wifi with a manual ip and use 188.8.131.52
7. Go to ps store
8. It will ask you to create an account or use existing. I was able to use my existing account, but only from this point. When formatting the card (if you have one, not sure how slim deals with the account link thing) if you try to use your account here you will be asked to upgrade before being able to download a psp demo).
9. Locoroco demo is no longer available but there are a ton of PSP demos still. Download and it will ask you to sign in and set a few preferences.
The steps are more or less in order. I'm sorry I didn't write it as I did it, I wasn't sure it would work. I will say that the only things that might be out of order are parts of steps, not the steps as a whole. I apologize again, however if you use this guide any part out of order will be obvious and you'll be able to succeed. It's solid enough to keep anyone with half a brain from making a mistake. I hope that I didn't write this SO late that nobody ever needs it.a