I was digging for like a week or so, because i have the same problem. ( i have 2g / gsm signal, but when i switch to wcdma (or 3g) only, i was getting no signal at all. (the circle with the line in it). My imei is not broken/missing, and from all the forums i've been digging i came to conclussion that there are several possible solutions as i think, but im not too deep into that matter, so im just sharing my thoughts, dont try these if you dont know what are you doing, i say again, im not completely sure if any of those gonna actually work.
1st - EFS Proffesional (along with Qualcomm NV Tools) - which can be found here, in xda. (The program itself has a ****load of options, and i dont have the knowledge to operate with it). Qualcomm NV Tools is a part of EFS Pro.
2nd - the secret code menu - Service Mode ( *#197328640# ) - I wasnt able to enter it at first, so downloaded the Shortcut Master (lite) (free in Play Store) and found it there, launched it with option 0 (launches a code with root priv) and i entered the service mode.) i've explored it, there are a lot of settings there, like backup, restore, rebuild, changing bands and so on and on and on, and somewhere inside it, there MIGHT be a solution inside those. I'd like to hear something more about those options from someone who actually understands them.
Other option is JIFF BOX, which i dont know how actually found, it seems that program requires qualcomm usb drivers for PC, and i think this is something like virtual box or w/e it is, i couldnt run it, didnt have time atm, but this program is given to wake up even completely dead sgs4 somehow, so why not bringing back the 3g?
And the last thing ive found - SRS - (found it in sammobile's forums. Some kind of imei/efs/baseband/etc restorer, reflasher or w/e it is. But this is paid program with free trial for unlocking the screen pattern. )
At last, you/me, can always go for a service with box for samsung phones and pay for reflash/repair. Is this the only solution?
Forgot to tell - im using i9505. simfree, no brands etc....