Would DES be secure with 128 bit keys? Assuming you only modify the key schedule so that each of a 128-bit key is used at least once, would DES be about as secure as other ciphers such as AES? I am not talking about 2DES/3DES or other drawbacks like performance etc.
No, DES* (which I'll call your "DES modified to use 128 bit keys") would not be as secure as AES; two reasons spring immediately to mind:


Block size; DES* would still have 64 bit blocks; most block cipher modes start to leak information when you get close to the birthday bound; for DES*, that'd be 32Gigabytes, which isn't that long for common use.  In contrast, AES (which has a 128 bit block size) has a birthday bound of circa 300Exabytes
Linear cryptanalysis; DES is known to be weak against linear cryptanalysis; depending on how you map the 128 bit keys to the DES* subkeys, DES* may very well be as well.  Of course, AES is known to be immune to linear cryptanalysis