Samsung Galaxy S: phone won't send or receive calls and text messages
I am suspecting, after reading the logcat and dump, the kernel killed off quite a few processes, whether its down to the ROM itself, or a buggy RIL (Radio Interface Layer), RIL is responsible for communicating with the cellular radio base-band firmware.

This is the excerpt from the kernel, showing Dolphin, Alarm Clock, Google Voice(?) getting killed off:

[125362.321461] select 2452 (ogle.android.gm), adj 8, size 5199, to kill
[125362.321481] select 2543 (.osp.app.signin), adj 9, size 3650, to kill
[125362.321495] select 2559 (pp.clockpackage), adj 9, size 4222, to kill
[125362.321512] send sigkill to 2559 (pp.clockpackage), adj 9, size 4222
[125363.255635] select 1225 (ek.TunnyBrowser), adj 7, size 19674, to kill
[125363.255657] select 2452 (ogle.android.gm), adj 8, size 5189, to kill
[125363.255671] select 2543 (.osp.app.signin), adj 9, size 3648, to kill
[125363.255684] select 2597 (gphone.acc.free), adj 9, size 3850, to kill
[125363.255699] send sigkill to 2597 (gphone.acc.free), adj 9, size 3850
[125364.339592] touch_led_control: 2 
[125365.378613] select 1225 (ek.TunnyBrowser), adj 7, size 19294, to kill
[125365.378646] select 2452 (ogle.android.gm), adj 8, size 5061, to kill
[125365.378664] select 2543 (.osp.app.signin), adj 9, size 3604, to kill
[125365.378681] select 2611 (ock.xtreme.free), adj 9, size 3969, to kill
[125365.378702] send sigkill to 2611 (ock.xtreme.free), adj 9, size 3969


This is the excerpt from the telephony, note the gap in time logged, last logged at 19:23:48.949 and 19:35:33.144:

01-13 19:23:48.949 D/RILJ    ( 2574): [14954]&gt; REQUEST_GET_NEIGHBORING_CELL_IDS
01-13 19:23:48.949 D/RILC    ( 2366): [14954]&gt; GET_NEIGHBORING_CELL_IDS 
01-13 19:23:48.949 D/RILC    ( 2366): [14954]&lt; GET_NEIGHBORING_CELL_IDS fails by E_REQUEST_NOT_SUPPORTED
01-13 19:23:48.949 D/RILJ    ( 2574): [14954]&lt; REQUEST_GET_NEIGHBORING_CELL_IDS error: com.android.internal.telephony.CommandException: REQUEST_NOT_SUPPORTED
01-13 19:35:33.144 D/RILJ    ( 2574): [14955]&gt; SCREEN_STATE: true
01-13 19:35:33.148 D/RILC    ( 2366): [14955]&gt; SCREEN_STATE (1)
01-13 19:35:33.152 D/GSM     ( 2574): [GsmMultiDCT] Stop poll NetStat
01-13 19:35:33.644 D/RILC    ( 2366): [UNSL]&lt; UNSOL_RESPONSE_NETWORK_STATE_CHANGED


Further on in the log related to telephony:

01-13 19:36:13.891 D/RILC    ( 2366): [14972]&lt; QUERY_NETWORK_SELECTION_MODE {0}
01-13 19:36:13.891 D/RILJ    ( 2574): [14971]&lt; SCREEN_STATE
01-13 19:36:13.891 D/RILJ    ( 2574): [14972]&lt; QUERY_NETWORK_SELECTION_MODE {0}
01-13 19:36:13.895 D/RILC    ( 2366): [14973]&lt; OPERATOR {AT&amp;T,AT&amp;T,310410}
01-13 19:36:13.899 D/RILJ    ( 2574): [14973]&lt; OPERATOR {AT&amp;T, AT&amp;T, 310410}
01-13 19:36:13.899 I/GSM     ( 2574): EVENT_POLL_STATE_OPERATOR
01-13 19:36:13.899 D/RILC    ( 2366): [14974]&lt; GPRS_REGISTRATION_STATE { 1,a7e9,007537ea,9}
01-13 19:36:13.899 D/RILJ    ( 2574): [14974]&lt; GPRS_REGISTRATION_STATE {1, a7e9, 007537ea, 9}
01-13 19:36:13.899 D/RILC    ( 2366): [14975]&lt; REGISTRATION_STATE {1,a7e9,007537ea,(null),(null),(null),(null),(null),(null),(null),(null),(null),(null),0}
01-13 19:36:13.903 D/RILJ    ( 2574): [14975]&lt; REGISTRATION_STATE {1, a7e9, 007537ea, null, null, null, null, null, null, null, null, null, null, 0}
01-13 19:36:13.923 I/GSM     ( 2574): &lt;Leo&gt; PrePLMN: 310410, plmn: 310410, ss.getState(): 0
01-13 19:36:13.923 I/GSM     ( 2574): handlePollStateResult(); regState: 1, mNewLuRejCause: 0
01-13 19:36:13.923 D/GSM     ( 2574): Poll ServiceState done:  oldSS=[0 home AT&amp;T AT&amp;T 310410  HSDPA CSS not supported -1 -1RoamInd: -1DefRoamInd: -1EmergOnly: false] newSS=[0 home AT&amp;T AT&amp;T 310410  HSDPA CSS not supported -1 -1RoamInd: -1DefRoamInd: -1EmergOnly: false] oldGprs=0 newGprs=0 oldType=HSDPA newType=HSDPA
01-13 19:36:21.298 D/RILC    ( 2366): [0001]&gt; OEM_HOOK_RAW (raw_size=6)
01-13 19:36:21.302 D/RILC    ( 2366): [0001]&lt; OEM_HOOK_RAW
01-13 19:36:21.306 D/RILC    ( 2366): [UNSL]&lt; &lt;unknown request&gt; {0}
01-13 19:36:21.306 D/RILJ    ( 2574): processing unsol response: java.lang.RuntimeException: Unrecognized unsol response: 11012


The NITZ (Network Identity and Time Zone) crops up a fair bit too, as shown below within the same telephony log, IIRC, NITZ handling was not exactly great up to ICS, in which a patch was made to handle the handling of the timezones (either roaming when browsing the net or something awry went wrong with the RIL:

01-13 19:13:19.035 D/RILC    ( 2366): sendUnsolicitedResponses: multi client index=2, fd=28
01-13 19:13:19.035 D/RILC    ( 2366): [UNSL]&lt; UNSOL_NITZ_TIME_RECEIVED {13/01/14,03:13:18-32,00}


The telephony errors shown, are sticking out like a sore thumb, and also down to the fact that Froyo 2.2, is old, and may not be able to handle whatever issue is with AT&amp;T that causes it. Also, AT&amp;T could have had their systems updated/upgraded, that is sending out extra telephony information/NITZ in a format that Froyo cannot handle and freezes.

Best bet would be to try a firmware update and see if that resolves the issue. 

Prior to doing an update, since the handset is rooted, best to make a backup of everything, use Titanium Backup to backup user apps and data, use SMS Backup &amp; Restore to save the SMS messages. It will be inevitable that the upgrade will lose root, but then again, it would be easy to do that after the upgrade.