PSExec has options to specify a username and password, which is required when running a task on a remote computer that requires access to network resources (otherwise PSExec is limited to local resources). Connecting with the appropriate account should give you the access you require: try psexec -u < username > -p
Additionally, the runas command runs a command (even cmd) with the specified privileges. I don't know how nicely it plays with PSExec due to the issue mentioned above, but use the following syntax to elevate priveleges:
runas /user:<domain>\<username> cmd
You will be prompted for a password; if typed correctly, you will be running in a new command prompt with the privileges of the specified account. The privileges may be limited by the privileges PSExec is running with, though.