If you get one of these calls, pretend to be a composite of the most idiotic users you speak to on the phone and take up as much of their time as possible.
You can drag the call out through the following techniques:-
1) Your on a slow computer and <program/webpage> is taking ages to load. You can easily stack up 15-30 seconds with this repeatedly.
2) Tell them their remote access program that they want to connect with has been blocked by your firewall. You can easily stretch it out for another 5 minutes with them trying to talk them through this before offering to uninstall it.
3) Tell them their program is blocked by your AV software. You can get another 5 mins from this, and offering to uninstall and then tell them it's asked to reboot and ask them if they want you to do it. That'll be another minute or two.
4) In case of emergency, feign an XP SP1/2 box, and claim that anything the scammer wants you to run gives you a "this computer needs SP3" error. and let him talk you through downloading SP3 so he can scam you. You know how long you can gain through this if you can keep the scammer on the phone.
You should be able to keep them on the phone for 15 minutes easily. 30mins is quite possible, and points should be awarded exceeding 30 mins or for getting the "engineer" on the other end to:-
1) sound audibly frustrated.
2) Scream or shout at you. Bonus points can be earned if you can sound like your upset at being shouted at enough to make the "engineer" feel guilty. Further points if you can calm him down enough to keep him on the phone only to repeat a few minutes later. Considerable bonus points if you can get his supervisor on the phone so your wasting 2 peoples time.
3) get the caller so frustrated that they end up taking the frustration out on people in the office at the other end, or just get so generally frustrated that they consider a new career in response.
My record is about 40 minutes before the phone was slammed down hard enough that it could have written off the handset, but i'm sad to say that I think i'm on a blacklist now. I've not had one of these calls for several years so I haven't had any opportunity to get a higher score.
Bastards. I was starting to enjoy those calls.